A pile can have no cards in it. In this case, you'll choose whether to put all the revealed cards into your hand or into your graveyard.

You (not your opponent) choose which pile to put into your hand and which to put into your graveyard.

In multiplayer games, you choose an opponent to separate the cards when the ability resolves. This doesn't target that opponent. Because the cards are revealed, all players may see the cards and offer opinions.