Entering a creature's square and AoOs

[Bauglir]

Is the attack of opportunity provoked for entering a creature's square for leaving a threatened area, or is it separate from that? If the latter, where's the rule located? A quick skim of Combat has proved unenlightening.

[kitep]

It's when you move out of a threatened square.

PHB, pg 175, under "Attacks of Opportunity"  (bold mine)

ATTACKS OF OPPORTUNITY
    During combat, you threaten all squares adjacent to yours, even when it’s not your turn. An opponent that takes certain actions while in a threatened square provokes an attack of opportunity from you. An attack of opportunity is a free melee attack that does not use up any of your actions. You can make one attack of opportunity per round. Actions that provoke attacks of opportunity include moving (except as noted below), casting a spell, and attacking with a ranged weapon.
    You provoke an attack of opportunity when you move out of a threatened square, except:

If you withdraw (a full-round action), opponents don’t get attacks of opportunity when you move from your initial square. If you move into another threatened square, however, opponents get attacks of opportunity when you leave that square.

If your entire move for the round is 5 feet (a 5-foot step), opponents don’t get attacks of opportunity when you move.

[kitep]

There are also other circumstances that cause an AOO when you move into an opponent's space.  The one I can think of is a Bull Rush, in which case it's the bull rush that provokes the AOO, not the moving - though since you have to move (charge) to do a bull rush, your opponents may be able to take their pick of which reason they get the AOO, but they're still limited to 1 per turn.

PHB, pg 154, under "Bull Rush"  (bold mine)

BULL RUSH
    You can make a bull rush as a standard action (an attack) or as part of a charge (see Charge, below). When you make a bull rush, you attempt to push an opponent straight back instead of damaging him. You can only bull rush an opponent who is one size category larger than you, the same size, or smaller.
    Initiating a Bull Rush: First, you move into the defender’s space. Doing this provokes an attack of opportunity from each opponent that threatens you, including the defender. (If you have the Improved Bull Rush feat, you don’t provoke an attack of opportunity from the defender.) Any attack of opportunity made by anyone other than the defender against you during a bull rush has a 25% chance of accidentally targeting the defender instead, and any attack of opportunity by anyone other than you against the defender likewise has a 25% chance of accidentally targeting you. (When someone makes an attack of opportunity, make the attack roll and then roll to see whether the attack went astray.)

Considering the 25% mis-chance, if they can get the AOO for you moving out of a threatened area instead of moving into the defender's space as part of a bull rush, they should do so.  But this would require them to threaten the square you move from, and not just the defender's square.

Edit - after re-reading this, I'm actually thinking they don't get a choice.  The get the AOO as part of the bull rush and not as part of movement, and so have to deal with the 25%.  I look forward to seeing what others say.

[kitep]

Overrun (PHB, pg 157, under "Overrun", bold mine)

If you’re attempting to overrun an opponent, follow these steps.
Step 1: Attack of Opportunity. Since you begin the overrun by moving into the defender’s space, you provoke an attack of
opportunity from the defender.

Like Bull Rush, this looks like the Overrun and moving into the opponent's space, not leaving the threatened area is what triggers the AOO.

[kitep]

Grappling (PHB, pg 156, bold mine)

Step 4: Maintain Grapple. To maintain the grapple for later rounds, you must move into the target’s space. (This movement is free and doesn’t count as part of your movement in the round.) Moving, as normal, provokes attacks of opportunity from threatening opponents, but not from your target.
    If you can’t move into your target’s space, you can’t maintain the grapple and must immediately let go of the target. To grapple again, you must begin at Step 1.

I would say that when grappling, moving out of the threatened area is what provokes AOO, not the grappling itself.

[kitep]

To clarify the previous 4 posts:

AOO is provoked when leaving a threatened square, unless doing a withdrawal (1st square only) or 5-foot step.
AOO is ALSO provoked when entering an opponent's square when doing a bull rush or overrun.

Opponents may have a choice of reasons of why they take an AOO, but they're still limited to 1 AOO per turn (and even Combat Reflexes still limits them to only 1 AOO against the same target, even if they have multiple opportunities).

[Bauglir]

Good to know, then. There's always been an unspoken understanding in my group, and it appears among the authors (given statements like "Since you begin by moving into a defender's space...") that this provoked an AoO, but I wasn't sure if it was because you are almost always leaving a threatened space in the process or of it was because of an independent rule.

[Jackinthegreen]

Creatures Tiny or smaller typically provoke AoO's when they enter another creature's square to attack. (See this page and search for Provoke.)

A creature initiating a grapple provokes an AoO unless it has Improved Grapple or is otherwise given an ability to avoid provoking.

[Kethrian]

Opponents may have a choice of reasons of why they take an AOO, but they're still limited to 1 AOO per turn (and even Combat Reflexes still limits them to only 1 AOO against the same target, even if they have multiple opportunities).

Actually, if you get multiple AoOs per round, you can attack the same target multiple times, so long as it provokes multiple times.  In the cases stated here, though, movement is a single provocation, regardless of which type of trigger is used.  An example of when a creature provokes twice would be moving within your threatened area but not actually leaving it, then making a ranged attack.

[kitep]

I stand corrected.  You're absolutely right.

PHB, pg 137, last paragraph (bold mine)

Combat Reflexes and Additional Attacks of Opportunity: If you have the Combat Reflexes feat (page 92), you can add your Dexterity modifier to the number of attacks of opportunity you can make in a round. This feat does not let you make more than one attack for a given opportunity, but if the same opponent provokes two attacks of opportunity from you—such as by moving out of a threatened square and then casting a spell in a threatened square—you could make two separate attacks of opportunity (since each one represents a different opportunity). 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. All these attacks are at your full normal attack bonus.