Home Run or Out? Baseball Rule Clarification

Question
I need to clarify this questions that I asked previously, so that there is no room for confusion.  An outfielder leaps up to catch a fly ball, catches it with part of his body over the wall, and his momentum carries him completly over the wall.  He does not drop the ball, but is no longer on the field.  Home run...or Out?  
Thanks!  

Answer
Brian,

In the situation you described, the batter has just been retired by a spectacular play turned in by the outfielder!

If the outfielder had jumped the fence, landed, then turned and caught the ball, the batter would be celebrating a home run.

Hope this helps!

Brian