How many major houses will have its downfall?

[Bael Abel]

There are enough Lannisters to continue the line, I am not worried about their future....

There are plenty of Lannisters of Lannisport, for now, but that doesn't mean that all of the enemies Tywin and Cercei have made (pretty much every great house but Arryn) won't see fit to pass The Rock to someone else.

I predict

-CR will be lost to the Lannisters until Tyrion wins it back purely though cunning, like Lann the Clever.

-House Arryn will be succeeded by either House Royce, or House -----, by way of Sansa's maneuvering, but not led by Sansa herself.

-Martell will hold Dorne by blood, if not by name.

-Highgarden will change hands a couple times before whoever wins the GoT will give it to one of their subjects.Maybe Sansa, if she make's the right allies. Tyrell will be reduced to a minor house much like House Connington

-The Stark name will survive through Rickon. Even if Jon Snow is Legitimized and released from his vows and made Lord of Winterfell, I don't think he'll survive the LN. I believe he'll die heroically fighting the WW from the walls of Winterfell after the Wall comes down

-Storm's End will go to Edric Storm, after (f)Aegon legitimizes him in order to win the Stormlands. If he keeps it, I'll be surprised, but I don't know who'll take it from there.

-The Iron Islands will go to a Harlaw through marriage to Asha Greyjoy

-Riverrun... I'd like to see it go to a Blackwood? Edmure's baby seems a solid candidate too, if Roslyn and her kid survive the war. I don't think CR is going to stay the safe place it has a history of being.