In a multiplayer game, if Zuko, Conflicted's owner leaves the game, Zuko, Conflicted leaves the game with them. If his controller leaves the game, Zuko, Conflicted is exiled (assuming that player wasn't also Zuko, Conflicted's owner).

When Zuko, Conflicted is under an opponent's control, his triggered ability will trigger in their first main phase, and they will make all choices for the ability.