I don't think Tyrion did it, although I wouldn't blame him. Maybe I missed it but who is King now?
I don't think the Queen inherits the throne, cause Cercei didn't get it after Joff's father died.
Fair point. Maybe one of the bastard children?
Edit - no spoilers, apparently it's already been noted last season but Joffrey has a younger brother. I had forgotten this. Don't know if he's also a product of incest. I assume it will pass to him. And House Tyrell would have no claim as the marriage was never consummated.