A lot of talk here about succession.
I have to point out the obvious:
Aerys II was succeeded by Robert Baratheon.
Robert Baratheon was succeeded by two Lannister boys who were not related to him.
Succession is “whatever” in Westeros.
Well, they were Baratheon boys by name because it was assumed they were the children of Robert and Cersei. It is still considered a dirty rumor that they were the products of Lannister incest.
“Robert Baratheon was succeeded by two Lannister boys who were not related to him.”
Shsssh...! Don’t say that out loud. The peasants don’t know they weren’t Baratheons!