A player want to shoot an arrow through a scroll that a NPC is holding. How would I calculate that?
If he's wanting to attack and damage/destroy an object, he'd have to perform a Sunder maneuver, using his BAB + Dexterity + other Attack Roll modifiers against the enemy's CMD. If successful, he deals damage to the object, which you subtract hardness and all that for, and if he brings the object's hit points to 0 or less, it's destroyed.
Although there's a rule example that says you can direct an attack at a potion (using the relevant AC), I believe that's more of a specific rule regarding potions provoking an AoO for drinking them, and that if you wanted to destroy the potion by normal means, you'd use the Sunder rules as I've described above.
Normally, you need to be in melee to sunder, but as the GM you're free to allow ranged sunders, especially in reasonable situations like this.
Would there be a size modifier for the size of the object?
Presumably, a tiny object, so +2? Size bonus.
that's what I figured. So I'll have him do CMD+2. Thanks for the advice. Now to go over to the game and give him the good news :)
I'd let it just be a sunder attempt against the targets CMD. This would, of course, be a one-off thing that the player can do assuming they had the initiative advantage or had prepared an action to shoot a scroll someone pulls out.
Basically, don't let them think they can sunder everything out of peoples hands or else you might find it impossible to use wands, potions and most other things as they sunder everything before you can use it.
This is a legitimate tactic. Just remember that piercing weapons do virtually no damage, and a scroll often has more than one spell on it. Poking a teeny hole in the paper is unlikely to ruin much of anything. Using deadly aim might be skinned as taking a hit on the scroll-rod, which falls apart and tears the scroll down the middle, but you're still doing half damage even then. It's just that half of 10 is a lot more than half of 5.