Lord Paramount of The Westerlands.
Lord Tywin Lannister is the Leader of the Westerlands faction. While Lord Tywin is not technically the king of the Westerlands within the book or television series, he does lead the largest army of the Lannister family, therefore it is more logical to have Lord Tywin "rule" the Westerlands rather than replace him with any of his family.
Tywin fields the largest army in-game.
Lord of King's Landing, Lannisport, and Casterly Rock, Harrenhal, Crossed Elms, and Pennytree.