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In WoT's case, Robert Jordan left behind 200,000 words and hours of dictation of drafts, fragments, book and chapter outlines and character information. He specifically instructed Tom Doherty and Harriet McDougall to find a writer to finish the final WHEEL OF TIME book and had just under two years from the diagnosis of his fatal condition to his passing to make preperations for that end.
With Middle-earth, no new information or fiction has been created by anybody other than JRR Tolkien. The posthumous works have been assembled by Christopher Tolkien out of JRRT's own writings, edited with detailed footnotes explaining exactly where the material has come from and why he chose a certain draft to use and not another. There has never been any posthumous creation of new material related to Middle-earth, just a certain amount of packaging and re-packaging of material JRRT left behind when he died in 1973. And Chris Tolkien has also released virtually all of the raw notes, materials and drafts so fans can judge for themselves if he's made the right calls or not.
DUNE is exactly what we don't want to happen. Kevin J. Anderson and Brian Herbert claimed that they had a significant amount of notes and drafts from Frank Herbert to work from. Later on, it was revealed that these claims were somewhere between extreme exaggerations and out-and-out lies, to the unrelenting fury of the DUNE fanbase. Frank Herbert's notes were very, very brief and thin (one sheet of A4, according to some) and consisted of a few thoughts for the planned seventh book in the series, certainly nothing at all for eleven (so far, with more coming) more books in the setting.
At the moment here and now, and GRRM himself has said this could change if he was halfway through the last book with the finish line in sight, there are no notes and no material to work from. Any other writer finishing the book would basically have to make it up, and their guesswork would be no more or no less valid than anything you or I or a million other fans could come up with in some forum discussion somewhere. That's what makes it fanfiction: it wouldn't be GRRM's vision or story on the page. With the Sanderjordan situation, we know that Jordan would have told the details of the story differently, but the events are what he had planned and he did write the final chapter of the series before he died, so that situation is a lot more faithful to his vision.
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Erikson is insufficiently talented to write a satisfying conclusion to ASoIaF. And before you complain, I would also say that GRRM is insufficiently talented to write a satisfying conclusion to any future MALAZAN series. They are very different authors with very different styles. Erikson is lucky in that ICE has a compatible style with his (if less florid), just as Jordan was lucky that Sanderson was able to adapt his style to match the other WoT books (if imperfectly). But Martin and Erikson write very differently with different focuses, and one writing in the other's world wouldn't really work.
The only author whom I think could write an ASoIaF book other than Martin is Daniel Abraham, who has a similar style and who has worked with GRRM on many other projects (including the ASoIaF comics). And Abraham, as a close friend of GRRM's, wouldn't even think about it without Martin's express permission or access to his notes and with some idea of where Martin was taking the story as it ended.