Umpire call at the plate

Question
QUESTION: If a batter has a 1-1 count on him and argues the next pitch to the point where the umpire ejects him from the game, is this batter automatically out?  If not, what happens to the count?  Does the replacement batter inherit the count?

ANSWER: I have never seen an actually ruling on a situation like this nor have I read anything in the rule book that would give me an answer. But if I was the umpire I would call an out based on the fact that he would be delaying the game in arguing the balls and strikes. That would make it so he finished his turn at bat and then was ejected afterwards, thus not complicating anything (too much). The team would then bat their next in line and have a replacement for the ejected batter on the next turn.

---------- FOLLOW-UP ----------

QUESTION: Ok, 2 outs, bases loaded, bottem of the 9th, score 2-1 in favor of the visiting team.  If in your senerio the batter is out, game over.  Bad sportsmanship.
Now say it's 1 out, you call the batter out for arguing, a new batter comes up, why penalize the pitcher by renewing the count?

Answer
It wouldn't be penalizing the pitcher by renewing the count. It would be helping the pitcher by giving him 2 outs instead of 1. It would be penalizing the batter for having bad sportsmanship in such a close game.

It states in the rule book that umpires are to have zero tolerance if coaches or players argue balls and strikes.