: Are the most successful authors like Stephen King and Jk Rowling all trade-published? I mean are the most famous authors usually trade-published or are there some self-published others that are

Professionals are used by the famous, and even the not-so-famous but successful.
Nearly all of them. The reasons are simple; really, publishing enough books to let you be a full-time fiction writer earning as much as you could doing any other job you are capable of doing requires highly specialized knowledge, experience, and an extensive list of professional contacts on tap.
To earn even a middle class American life-style writing fiction, about K a year, you must sell tens of thousands of copies. To be specific, the typical royalty for a paperback is 15%, the typical price is .95 (.95 to .95); so the royalty per book is .39 (.09 to .69). So, not considering cuts that do happen, you need to sell 21,000 books a year to earn K per year.
Here is link on a publisher's P&L viewpoint.
That just isn't easy, it is its own entire business enterprise that requires full-time attention and an organization that knows what it is doing to negotiate with producers, shippers, bookstores, online venues, advertisers, artists, etc. Not to mention TV or film producers, scriptwriters, audio book voices, foreign venues, merchandise rights (for toys or T-shirts etc).
Real authors love the creative process, they don't want a full-time job managing a production and sales enterprise. Publishers earn their money. To be a successful author, you need to sell tens of thousands of books every year, and each one is not an evergreen source of income. One is seldom enough, the truth is that multiple books have synergy, even if they are not a series. Each sells the others. If you are going to be famous, you need to spend the majority of your time in the year writing, and let other people promote, produce, and sell, which is what they can do far better than you can because they are trained professionals.
The more things you try to do yourself, the more things there are for you to suck at. To be ignorant, and unaware of the culture, to be ripped off by a fraud that steals your money and/or work, to be truly incompetent at a critical juncture and cause yourself grief.
Forget the "success" stories of self-publishing, it is like studying lottery winners for clues about how to win the lottery. The success stories in self-publishing got lucky, with what they wrote, with who they met, with their timing and when they wrote it, with who they found for artwork, with every arbitrary choice they made along the way.
Look instead at the typical experience; which is far more likely to be your experience. Here is a post on the average earnings of a self-publishing author on Amazon. (Less than 0).
Being greedy is recipe for getting almost nothing. Take 15% of a $million, or 100% of 0, its up to you.

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I think famously JK Rowling submitted Harry Potter to something like 20+ publishing houses, and only got picked up by a lucky accident - one editor plucked it out of the slush pile to give to their kid to read and didn't think any more of it until the child pestered them for more.

JA Konrath is a huge advocate of self-publishing. IIRC his story is that he was paid (for his series of novels) by the big publishers approx 0,000 ... which sounds like a lot ... until you realise that it's spread out over ten years. (So k per year)

But then of course he also had to travel around promoting his books, and so after deducting travel expenses (most of which he had to pay himself) from the k/year he was actually making below average wage - while working extremely hard for the privilege.

So then some of his stories reverted back to him (a standard publishing contract used to have that if they decided not to publish it (read as: not do another print run) then you got the rights back and could shop it around yourself - with an implied "haha, good luck with that").

So he published them on Amazon, and they started selling. Not necessarily in huge numbers (the average e-book sells 30 copies - but obviously Konrath's had had the advantage of an existing (if small) fanbase, as well as having been beaten into shape via professional editing).

Also, he had a back catalogue of about 60 books at that stage (IIRC). So in that first year he made as much from self-publishing his back catalogue on Amazon as he had in ten years with the print and paper industry.

Not entirely surprisingly, he thinks (and advocates that) Amazon is awesome and the traditional publishing industry sucks balls.

Also, not entirely surprisingly, publishing contracts now want to include the publisher getting the rights to e-distribution, and thus the rights will never revert back to authors anymore (because it's always 'available' online, even if the publisher isn't pushing it (which they have no incentive to do at that point)). Hmmm....

So let's examine the case of someone with sixty e-books versus someone with one:

a reader is sixty times more likely to find one of your books
if they like it there's 59 more to buy
word of mouth; you have 60x more exposure so you're 60x more likely to be recommended

So this is basically 60^3 or a leverage factor of 216,000:1

That's a really powerful advantage.

With Konrath for instance, if someone was a fan of his work and had maybe bought or read 4 or 5 from the bookstore or library, suddenly they were able to access the remaining 55-56 books. (I'm sure we've all had that frustration where you can find almost but not all of the books in a series of N books - well e-books are perpetually available so that problem goes away)

Subsequently Amazon have changed some of their platforms (e.g. KDP) from being egalitarian to having special bonuses for the best sellers. This makes them much less attractive for building a platform as compared to people with an existing platform.

Also Amazon's 'solution' to becoming popular is to tell authors to make their books available for free and then to make it up in volume.

If you have one book and you give it away for free you're not even treading water. Even if I became your biggest fan and wanted to give you money I couldn't in that scenario.

On the other hand, if you have say two books and you give the first one away, then people can still pay you money when they buy the second book.

I might have the wrong end of the stick, but I think Konrath rotates through about half a dozen books (sprinkled throughout his oeuvre) which are usually available for free as 'tasters'.

Also, Konrath didn't stay still and rest on his laurels. He continued to make more books, expanding into different genres (not necessarily under the Konrath name (cough bodice rippers uncough (and think about the success of romance as a genre before you pooh-pooh that concept - if romance outsells everything else put together there are obviously things to learn or consider unless you hate money and success))).

Also he collaborates aggressively and continues to promote his platform, and the platforms which support his platfrom (Amazon, paying an editor yourself if you're going to self-publish etc.).

That's one of the key things - if you hate self promotion then why even consider self-publishing?

NB: I think Amazon is dishonest in a broken way - I self published 6 novellas and sold over 200 copies (I can say this confidently because I know most of the people who bought them) (so I beat the average, yay me) and each one (after tax) should have paid approx 27c, but the total Amazon paid me was 23c for the lot.

It's a bit like google and the youtube thing. They tell you your video was viewed N times and so therefore you earn X ... but they are the only ones who know the true value of N (for sufficiently large values of N) ... and the system they control incentivises them to lie about it so they can keep more of the ad revenue.

Anyway, if we assume an n-squared or n-cubed relationship between number of (good quality) ebooks you publish and your success at self-publishing, then I think that probably somewhere in the 20-30 book range is where the break even (e.g. pay for your rent) point is.

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Authors have become famous while self-publishing, but famous authors rarely stay self-published for long

Two examples in the recent past:

Andy Weir self-published The Martian in 2011. He posted it in serial format on his website, and later published it as a 99 cent Kindle book. It rose to the top of the Kindle's best sellers list, and in 2013 he sold the rights to Crown Publishing, a subsidiary of Random House, who released it in hardcover and paperback, where it once again skyrocketed to the top of the charts. In 2015, the movie was released and succeeded critically and financially.

50 Shades of Gray began life as a Twilight fanfiction. The author, E.L. James, subsequently removed it from the fanfiction sites and posted it on her own website. It was published by a small Australian web-publisher, The Writer's Coffee Shop, in 2011. In 2012 the series was picked up by Vintage Books, a subdivision of (once again) Random House. It too is now a movie (series).

Publishing a book is hard

The barriers today are a lot lower than they used to be, since a single uploaded file can be downloaded billions of times. But if you want to enter the realm of physical books, things are a lot harder.

You have to find a printer who will print you thousands of books. And you have to find the money to pay the printer, because they're going to want payment upfront, even though you're nearly broke because you're an author who is living off of ebook sales. Then you need a place to store these books, because they aren't going to all be bought immediately. Then you have to contact bookstores so that you can sell your books to them. Then you have to ship the books to the bookstores. And each one of those steps have innumerable details and complications and things you aren't prepared for.

Successful authors tend to be successful for one major reason - they are good at writing books that people want to read. Also, they tend to like writing books. This other stuff? The desire and the ability to handle these things are much scarcer. Even if it wasn't, the competence of one brilliant author is far outshone by the experience and resources a major publisher can bring to the table.

Publishers love books that have already been proven successful. Authors love publishers that can take the heavy lifting off their hands so that they can go back to doing what they love. So best-selling books rarely stay self-published for long

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Usually they are. Writing and marketing at that level is very difficult. You have to do more than one job well. The self published people that I know about are either niche (not mass market) or networked well within their field to piggy back to success. That last comment is not a derisive comment. If there is a wave, by all means surf it.

The point here is that to be famous you have to enter the main stream consciousness. It's very difficult for word of mouth alone to get you past all the gatekeepers and into the public eye. Not impossible, but if you do something well and it is noticed then enough people will swamp onto that idea that it's not as likely to work the next time, even for the initiator.

If you don't go traditional publisher, you still need a way to grab attention and you'll have to do all of the work. Traditional Publishers are attention grabbing machines with proven success of maintaining and providing material for that attention. They are built to do it for the long term (mostly), whereas an individual author on their own will have to become a publisher (in addition to becoming a writer) to succeed. Even if you don't go traditional publishing, you'll find yourself managing all of the duties (or all of the people who perform those duties for you) to be successful.

Editor
Proof Reader
Layout +/- cover & art
Publicist +/- social media
Marketing
Printing
Legal (Rights)
Translation/Foreign Communication

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