The rhetorical question underlying is when does a pitch stop being a pitch? In fast pitch, it is still a pitch (thus the pitcher is responsible for the results) until it hits something foreign to the field (excluding the field); if it touches the bat, it becomes a batted ball, if it touches the catcher, it becomes a live ball in play, if it touches the batter, it becomes a dead ball and HBP, if it touches something outside the field, it becomes a dead ball and a one base award (to all runners).
For slow pitch, the same rule applies, excepting the base awards (if no stealing), and that the pitch also ends if it hits the plate or the ground in front of the plate.
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