Ejection after the game.
 

Saw this on MLB highlights today. End of game called third strike. As player and PU walking off the field, player is arguing and umpire tosses him. The game is already over. I understand that umpires are still in charge until they are off the field and out of sight. But what are the consequences of this after the game ejection? Was it just symbolic?

In MLB, I would say it is just symbolic. The umpire is not going to take all the chirping before, during, or after the game. He was just making his point.

However, I don't know all the intricacies of ejections in MLB, so maybe an ejection gets an automatic fine?

OBR 9.5.2-3 Par. 4. If a player or coach receives a post-game ejection they must proceed directly to the club house and are NOT allowed to observe any part of the remaining game. They are to be placed under strict observation for three hours and write three hundred times, "I will be nice to umpires." For failure to complete their assignment in the required time limit, they shall be sent home until the next game. If they should happen to pass "GO" they shall receive $200.

Players and managers are still subject to league discipline, inlcuding fines, for post game ejections.

It's worth doing. Here is my experience. A player behaved in a way that deserved an ejection after the final out of the game. I ejected him and I wrote an ejection report. The league chose to suspend him one game considering his behaviour in previous games. Had I not ejected him. The league might not have been aware of the situation.

Jay, I had the County director of HS sports do it for me last season.
HS County Championship game. Last batter of the game takes a thigh high curve ball down the middle. I ring him up. Of course the winning team all rushes the mound and jump on their pitcher and celebrate. Fans are cheering ect. The batter decides to stand in the box and really give me an earful, but me and my 3 partners just walk off the field, I didn't eject him. Couldnt reallty hear much of what he was saying, plus I earlier ejected his Coach. Little did I know that the Director of HS Sports was watching the game. He emailed my scheduler, who fwd it to me. He said a suspension was coming for the coach and the last batter. They both missed the first game of the State Playoffs.