[FrankWakefield]

As I understand it, the home team owns the baseballs until the plate umpire asks for them. Once he asks for them, they go to MLB. As soon as the game ends, whoever has a baseball owns that baseball.... the home team owns the ones they still have, the plate umpire owns the ones in the bag, and whoever has the ball as the last out is made or winning run scores gets that ball.

To appreciate this, watch the plate umpire in the 9th inning. Before the inning starts he'll get 2 or 3 balls to fill his ball bag. Then, sometimes, with 1 or 2 outs, he'll turn to the home team dugout and hold up 4 fingers. Out runs the batboy with 4 baseballs. Then the last out is recorded. Once in the umpires' room, the plate umpire hands out balls to the rest of the umpire crew. They then give the balls away, or swap them for drinks or a meal back at the hotel after the game. (I apologize to all MLB umpires for letting that 'outa the bag', but it is so beautiful to see those 4 fingers flashed with 2 outs in the top of the ninth, when the plate umpire is standing there with 2 or 3 baseballs already in the bag.)