[BBDodge]

Originally Posted by bitontheslide

the baratheons have no claim on the throne given that Robert's entire reason for taking the throne was a lie

And they are now an extinct house. Only bastards.

Other extinct houses: Tyrell, Martell

Legitimate heads of remaining major houses:

Targaryen: now Aegon/Jon
Lannister: should be Jamie but big sis took the Crown
Stark: Bran (declined); Sansa
Tully: Edmure (still a prisoner?)
Arryn: Robert (a sickly child)
Greyjoy: Euron (likely to be deposed very soon)