The Antagonist is completely and totally dependent on The Protagonist for its existence. This is because he or she exists for the purpose of opposing the efforts of the Protagonist. They don't have to be a Villain, or even morally objectionable in any sense (though they often are); they merely have to oppose the Protagonist. The Antagonist usually provides the conflict and thus the story. Because of this, the Antagonist is about as Omnipresent as the Protagonist, though there are stories that have No Antagonist.