I was watching baseball highlights last night and saw??? Paul Lo Duca tag out the runner at the plate. The ump called the runner safe. In the heat of the moment Lo Duca threw the ball into the ground. He was promptly ejected from the game. After being ejected he picked up the baseball.

My thought/questions. I did not see the umpire call time. I could not see if any of the other umpires called time. For this exercise, let's assume no umpire called time. So, my questions are:

If an ejected player touches a "live" baseball, what happens? If a runner attempts to advance while the ejected player has the ball, can he throw him out? Is it interference? Is the ball dead as soon as an ejected player touches it? Does an umpire have to call time before ejecting a player? Can an umpire eject a player while the ball is "live"? Is "time" automatically assumed when a player is ejected?

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I did a little research and discovered MLB Rule 9.01D:

Each umpire has authority to disqualify any player, coach, manager or substitute for objecting to decisions or for unsportsmanlike conduct or language, and to eject such disqualified person from the playing field. If an umpire disqualifies a player while a play is in progress, the disqualification shall not take effect until no further action is possible in that play.

I thought I would still post my original question to share with everyone.