From the rules, I can see that when killing a character causes a tie, the player taking the action decides who gets the banner.
Forst question here is, what if that tie is with 0 cards? Killing the only character of that family taken so far. Does the banner just return in the center, or you resolve a tie woth 0?
Even more specific, since Jagen H'ghar can kill 2 characters and there are only 2 Tully characters, what happens with the banner in this case?
You should feel ashamed for even having such evil thoughts. I can't wait to do these things to someone in the game.