The ball is dead and all runners advance one base.
I just wanted to add onto this answer. When this happens the ball is a live ball until the runs advance a base. i.e if the ball never touches the ground and gets stuck in a jersey it would could as a lineout/fly out and the batter would be out, then it is a dead ball... if somehow it happens on a ground ball a force out can be made, but a batter cannot be tagged out
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It depends on how he leaves the playing field. If the fielder catches the ball in flight, and falls out of the playing field between homeplate and the yellow line on the wall (foul territory), the batter-runner is out as long as the player maintains full, controlled posession of the Baseball. However, if a player catches a ball and falls out of play over the yellow line signifying a homerun, the play should be ruled a homerun, but specific ground rules may be in effect to rule the batter out.
Yes as it is still caught on the fly, without touching the ground.
Depends on your definition. If a fly ball is caught in "Foul Ground", then yes it is an out.
Some leagues, for safety reasons, have an "out of bounds" area beyond foul territory. If a ball is caught there, there is no out and it is considered a foul ball.
Of course not. Once the ball hits a fence or a wall it is the same as if it hit the ground.
yes, assuming it's caught by one of the 9 players on the field.Anything that's caught is a out.