I have read through the acrobatics threads where you can tumble through a person's square that they occupy so long as you beat their CMD with your check. The consensus also seemed to be that if you failed you check, you stopped in the square in front of that person.
How about if you try to use the acrobatics skill to move past a person's threatened square, but not the one they actually occupy. For example, a Fighter is using a polearm and threatens 10ft away from themselves. A Thief wants to use acrobatics to move through one or more squares threatened by the Fighter.
1) Do they have to roll for each threatened square they move through?
2) If they fail, do they stop moving?
3) Could a person just choose to run through the threatened squares, not using acrobatics, knowing they will provoke an Aoo. Would their move be stopped if the Aoo hit them?