Home Run Catch Rule: Out or Home Run?

Question
Recently I saw a play where a fly ball was caught by a diving out fielder (at the fence/over the fence) and the player went on over the fence with the ball. Would it be considered a home run or an out!

Answer
Mark,

It is an out.  If the player's momentum brings them into the stands (either on a foul ball or a homerun) after catching the ball, the catch stands.  What can't happen is that the player runs into the stands and then catches the ball.  That would still be a home run.

You see it much more frequently on foul balls.  The player is in play and reaches in for the foul ball, catches it, and then falls into foul play.  Still an out.

Hope this helps!

Brian