If you have improved overrun, start right next to a creature, attempt an overrun (no AoO because of improved overrun) and the creature lets you pass (so no CMB roll), does the creature get an AoO when you leave the square it occupies and move next to it on the other side from where you started? What if you keep moving, does it get an AoO because you moved through the threatened square on the other side?
Let's say you start 10' away from a creature without reach, is the AoO for an overrun the same as the AoO for moving through the threatened square between the two of you? So if you have improved overrun, does the creature get an AoO? If you don't have improved overrun and it has Combat Reflexes, does it get 2 AoOs, one for your movement and one for attempting an overrun?
What if there's a second creature next to the first. Can you combine Tumble (Acrobatics) with an Overrun to avoid AoOs from the second creature due to your movement? Or for that matter, can you use Tumble (Acrobatics) while moving before and after an Overrun to avoid AoOs from an overrunned creature that simply let you pass and can't knock down?
If you tumble up to a line of opponents, do an improved overrun and then keep tumbling, would you do a single skills check against each opponents CMD (+2 for each additional opponent that threatens) without the penalty for moving through an enemy's space, and a CMB check for the overrun, unless the opponent you move through chooses not to oppose your move, all without provoking an AoO?
Based on some reading (both PF rules and http://www.dandwiki.com/wiki/SRD:Overrun), here's what I believe:
1. If you have improved overrun, "targets of your overrun attempt may not chose to avoid you."
2. If you do not have improved overrun, the opponent gets an AoO when you attempt to leave the square right in front of him (to move through his square). That move AoO is the "overrun AoO"; the AoO provoked by an overrun attempt isn't a distinct type of AoO, it's a move AoO. There are no other possible AoOs from that opponent afterwards because:
"Moving out of more than one square threatened by the
same opponent in the same round doesn't count as more
than one opportunity for that opponent. " Improved overrun nullifies that AoO and subsequent moves do not provoke from that specific opponent.
3. If the opponent has reach, he gets an AoO when you move through a threatened square before making the overrun attempt. Improved overrun doesn't protect against that AoO. You would need Spring Attack to avoid that AoO, or alternatively you can tumble through the area threatened by the reach of the opponent. I *think* you can overrun as part of a Spring Attack.
4. Tumbling up to a defender that's part of a perpendicular line of defenders, then making an overrun, and then tumbling away isn't going to help against the AoO provoked when you leave the square in front of the defender. This is because even if you have improved overrun, all the other defenders that threaten that area will still get an AoO. You might as well just try to tumble all the way or just forget it and soak the AoOs.
5. The feat Mobility may be a good idea for when making an overrun attempt through a line or group of defenders.
3. If the opponent has reach, he gets an AoO when you move through a threatened square before making the overrun attempt. Improved overrun doesn't protect against that AoO. You would need Spring Attack to avoid that AoO, or alternatively you can tumble through the area threatened by the reach of the opponent. I *think* you can overrun as part of a Spring Attack.
You can't overrun and spring attack. They are two different standard actions.
Interesting situation that of a reach weapon wielder. If you are adjacent to him he doesn't get an attack of opportunity as he is not threatening you (except if you move more than 10'+ after going through his square). If you begin your action far from him he gets an AoO though you have IO. In any case, IO is useless versus him.