More speculation.
Tyrion is motivated to find Tysha and to exact his revenge upon Cersei. His potential allies are the Starks, the Targaryens, and the Martells. Well, the Lannister breach with the Starks is beyond restoration even with Tyrion's marriage to Sansa. The Martell's would love to have the true heir to Casterly Rock on their side, though it would seem hypocritical to back Myrcella's claim to Westeros while denying Cersei's to Casterly Rock. Tyrion could go to Dany, but why should she accept him? Tyrion somehow must find out that Tywin is not his father.
I think the theory goes like this... Joanna Lannister (Tywin's wife) was raped by Aerys when Tywin quit as Hand. Joanna, knowing that telling Tywin (who suffered no slights to House Lannister because Lannister's pay their debts) would mean war between Lannister and Targaryen, thought that the Lannister's would have been utterly destroyed and so she kept silent. Tyrion's fascination with Dragons and Fire, his mismatched eyes, and Tywin's refusal to acknowledge him are seen to be possible proofs.
Who knows the truth? Varys, Jamie, Kevan, the witch of Horn Hill, Magister Illyrio, and Maester Aemon seem to be possibilities.
I think more bastards of Robert's will surface. I think Hodor is one of them.
Sansa, disillusioned with the knights, lords, and ladies of the realm, will find her true love and true knight in Brienne. Of course, this will be after Littlefinger has taken her to wife. Littlefinger and Tyrion will both be able to make claims to Winterfell. But, Sansa, hating Littlefinger, will figure out that his obsession with Cat is his one and only weakness. She will start to use this to destroy the Lannisters and Littlefinger.
Sansa will later find real romantic satisfaction with Dany. Both are lovelorn, disillusioned, "older, but wiser", humiliated, and mistreated girls.
The Hound will flee Westeros, after being found and aided by some Targaryen loyalists, Darry or Dayne men most likely. He'll find his way into Dany's employment.
Poor, sweet, little Tommen will meet with a hideous death. Melisandre, Doran Martell, and Beric seem likely candidates.
I read somewhere that Lancel died, but was resurrected like Beric and Cat. Hmmm. I kinda like that.
Jamie will not let another King die without giving his own life first. He now is his own man since his father, lover, and brother have abandoned their holds over him. He may even remember his oath to Cat and do more for Sansa than sending Brienne after her.
Loras does not seem to like women. I think Varys will introduce him to some of the young men of the court, say, Podrick Payne or Tyrek Lannister.
Jorah is indeed in utter misery. He has nothing left. Will he take the black? Or will he try his luck with the Dornishmen or Victarion Greyjoy?
Daario is not long for this earth. Dany, her bloodriders, or Barristan will soon take his head.
Dany will not be content with one city. She'll remember the atrocities being commited in the other slave cities and she'll soon reign over Astapor, Mereen, Yunkai and all of Slaver's Bay.
Look for some Dothraki Khal (Jhaqo or Pono) wanting to gain favor with the crones of Vaes Dothrak. He'll assault Dany's new realm.
Somehow, Stannis, the rightful heir, will make contact with Beric, the defender of Robert's people. Ned Dayne will then become a Stannis man.
Rickon is more of an important pawn with each Stark death. He will foster at Greywater or be taken captive by the Boltons or Stannis. Or in an extreme move, Osha will actually get him down to the God's Eye. They will find Nymeria and the children of the forest. It seems that maybe Howland Reed has actually been to the Island of Faces in the God's Eye. He might take or send someone to take Rickon there for safekeeping.
Again this is speculation. Since Martin seems to delight in breaking the conventional rules of heroic fantasy, I thought I'd follow with some strange ideas.
