The ball is dead whenever the umpire calls "time", whenever it goes out of play, when it becomes a foul ball, whenever a pitch hits a batter, or whenever a batted ball hits a runner (and a few other circumstances). It doesn't matter whether the pitcher has it or not. On the other hand, it can't be put back _in play_ until the pitcher has it and is on the rubber.
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It depends. If the ball hits the umpire in the mask and stuns him. He will most likely call a dead ball or time. If he doesn't thoug. It is a live ball and still in play.