The card is exiled face up. Each opponent will know what the card is when deciding whether to have you put it in your hand.
2011-06-01
If no opponent has you put the card into your hand, the card remains exiled.
2011-06-01
In multiplayer formats, your opponents each make the decision in turn order.
Search your library for a card, exile it, then shuffle. Any opponent may have you put that card into your hand. If no player does, you draw three cards.