Greater Trip and Ki Throw

Benefit: You receive a +2 bonus on checks made to trip a foe. This bonus stacks with the bonus granted by Improved Trip. Whenever you successfully trip an opponent, that opponent provokes attacks of opportunity.

Normal: Creatures do not provoke attacks of opportunity from being tripped.

Benefit: On a successful unarmed trip attack against a target your size or smaller, you may throw the target prone

in any square you threaten rather than its own square.
This movement does not provoke attacks of opportunity, and you cannot throw the creature into a space occupied by other creatures.

If a creature has both Greater Trip and Ki Throw does he get an attack of opportunity for throwing the creature?

It looks like he does, the Greater trip would trump the no AoO of Ki Throw?

Whenever you bull rush an opponent, his movement provokes attacks of opportunity from all of your allies (but not you).

Benefit: When using the Ki Throw feat, you may throw your target into any square you threaten that is occupied by another creature. Make a bull rush combat maneuver check with a –4 penalty against the secondary target. If this check succeeds, the thrown creature lands prone in the secondary target’s square, while the secondary target is pushed back and knocked prone in an adjacent square. If the check fails, the thrown creature lands prone in the nearest square you threaten adjacent to the secondary target.

Now what if the creature(T) has Greater Trip, Improved Ki Throw, and Greater Bullrush. With an ally (A) at his side and an enemy(E) infront of each of them.

would look like
EE
TA

_EE (both now prone)
TA

If you have Greater Trip and Ki Throw and you trip someone, two things happen:

First, the opponent is tripped (knocked prone). Because of Greater Trip, this gives you an attack of opportunity.

Second, you can relocate the opponent to a threatened square. Even though your opponent is moving through threatened squares, this movement doesn't provoke AoOs.

The tripping and the movement are two separate effects. So, no, Ki Throw doesn't cancel out the AoO you get via Greater Trip.

I don't know about your second scenario. I could see it going either way. It hinges on whether or not the combat maneuver check that occurs when using Improved Ki Throw is an actual Bull Rush attempt or not - my opinion is that it DOES count as a Bull Rush, and thus triggers AoOs via Greater Bull Rush.

If he Improve Ki Throws one enemy into the other would the thrower get 1 AoO on the one he is throwing and his ally get 1 AoO for the creature thrown and 1 AoO for the creature bullrushed?

Assuming I'm correct that the combat maneuver check in Improved Ki Throw counts as a proper Bull Rush, in your example this is what would happen:

1. The first enemy is knocked prone; if the thrower has Greater Trip, this triggers an AoO from the thrower.
2. The first enemy is moved into the second enemy's square. This does not provoke AoOs from anyone.
3. The second enemy is bull rushed (with a -4 penalty); if successful, the enemy is pushed one square away, which provokes an AoO (via Greater Bull Rush) from the ally, since the enemy moved through a threatened square. The enemy is also knocked prone, but I don't see anything about this triggering AoOs.

The thrower cannot get an AoO against anyone. This is because AoOs are done when it is not your turn and the actions that (potentially) provoke happen on T's turn. Any adjacent allies, however, might be able to make those AoOs. I'm not sure which feat's text is the trump card, that of Ki Throw or Improved Trip/Improved Bullrush, but if those actions provoke, A really ought to have Combat Reflexes (to take advantage of the extra AoOs).

EDIT: It appears, after a careful re-reading of the AoO rules, that I am mistaken. There is nothing in there that states that AoOs can't be taken on your own turn. In my games, we have ruled that AoOs are Immediate Actions, which can only be taken when it is not your turn.

It seems your thrower would get to take his attacks too.

1. The first enemy is knocked prone; if the thrower has Greater Trip, this triggers an AoO from the thrower.

And the throwers ally would get an AoO. Since Greater Trip says "...that opponent provokes attacks of opportunity". Attacks is plural so provoking from anybody that the creature is in its threat range.

Therefore if the ally has combat reflexes he would get one for the enemy being tripped and one for the enemy being bullrushed. While the attacker gets only one from the enemy being tripped.

Chris P. Bacon wrote:

1. The first enemy is knocked prone; if the thrower has Greater Trip, this triggers an AoO from the thrower.

And the throwers ally would get an AoO. Since Greater Trip says "...that opponent provokes attacks of opportunity". Attacks is plural so provoking from anybody that the creature is in its threat range.

Therefore if the ally has combat reflexes he would get one for the enemy being tripped and one for the enemy being bullrushed. While the attacker gets only one from the enemy being tripped.

Oh, wow, you're right. I thought it was only for the tripper, but I was wrong. Good call!

(I'm not concerned with GBR, just KT and GT.)
Are you sure the AoO from Greater Trip happens before the throw? Could you not throw the opponent first, and then have it provoke the AoOs?

"On a successful unarmed trip attack...you may throw the target prone..." "Whenever you successfully trip an opponent, that opponent provokes attacks of opportunity."

Since you're throwing them prone, does the AoO-provocation happen (a) straight after the successful CMB roll, or (b) when they go prone? If it's (b) when they go prone, the AoO would be provoked after the throw, no?

There will be advantages and disadvantages to each event order, I just want to make sure I'm getting it right.

(I'm not concerned with GBR, just KT and GT.)

Are you sure the AoO from Greater Trip happens before the throw? Could you not throw the opponent first, and then have it provoke the AoOs?

"On a successful unarmed trip attack...you may throw the target prone..." "Whenever you successfully trip an opponent, that opponent provokes attacks of opportunity."

Since you're throwing them prone, does the AoO-provocation happen (a) straight after the successful CMB roll, or (b) when they go prone? If it's (b) when they go prone, the AoO would be provoked after the throw, no?

There will be advantages and disadvantages to each event order, I just want to make sure I'm getting it right.

There is no "right" answer in this instance, as the rules are silent on the issue. Since you (the tripper/thrower) are the one who gets to (a) make an AoO and (b) move the prone target to another square, I think it's perfectly reasonable for you to choose which one you want to do first.

HOWEVER, anybody else who could AoO the tripped character would have to do it at the instant of them being tripped, BEFORE they get moved, because they have to be threatening at the time the trip occurs. If it's a creature with big reach, you could maybe argue that they should get to take their AoO before or after the throw, but that's a judgment call.