Let's say I have a flying monster grappling a player in the air. It drops the player as a free action. As a result, the player moves out of its threatened area. Does my monster get an attack of opportunity?
I thought that at first as well, but I wasn't able to find any rules supporting it. Most things have a little statement saying "this movement provokes" or "this movement doesn't provoke", but here there's nothing. Specific trumps general, but there doesn't seem to be a specific in this case, and the general is that moving through threatened squares provokes.
I don't have something specific to falling, but by analogy to Bull Rush and Trip, you don't prove when you get Bull Rushed or Tripped unless whoever did this to you has the Greater Bull Rush or Greater Trip feat (and some other combat maneuvers are also like this), so probably you shouldn't provoke for falling unless the dropping monster had a Dropkick feat or something like that. I was going to say Greater Reposition could work for this, but I just looked it up, and it specifically excludes the repositioner from being able to take AoOs, although the repositioner's allies can take AoOs if they are in the right place.
I don't have something specific to falling, but by analogy to Bull Rush and Trip, you don't prove when you get Bull Rushed or Tripped unless whoever did this to you has the Greater Bull Rush or Greater Trip feat (and some other combat maneuvers are also like this), so probably you shouldn't provoke for falling unless the dropping monster had a Dropkick feat or something like that. I was going to say Greater Reposition could work for this, but I just looked it up, and it specifically excludes the repositioner from being able to take AoOs, although the repositioner's allies can take AoOs if they are in the right place.
And the Improved versions have to call out that they don't provoke, which implies that provoking from involuntary movement is the norm. It can be seen both ways really, which is why it's tough to make a straight call.
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Specific trumps general, but there doesn't seem to be a specific in this case, and the general is that moving through threatened squares provokes.I'd say that plummeting doesn't provoke, using a different general rule - that things that are 'not an action' do not provoke. Plummeting's a natural hazard, not an action of any kind.
(And yes, I know that it opens a weird corner case in which a creature with Flight 80, doing a 'run' straight down and gaining the dive speed bonus, would suffer an attack of opportunity despite moving faster than somebody who's falling at terminal velocity.)
Looking more closely, I think you may be right.
Provoking an Attack of Opportunity: Two kinds of actions can provoke attacks of opportunity: moving out of a threatened square and performing certain actions within a threatened square.
Since falling is not an action, even though you would move through threatened squares, it wouldn't provoke.