The reason I chose these, out of the several options I own, is because they're the simplest. I can describe how to run a chase scene in only a paragraph or two. Of course, the price of that simplicity is that they are fairly rules light, and require some GM adjudication and judgement calls.
Anyway, here goes:
When exactly a withdrawal becomes a chase is up to the GM, but clearly if one character (or monster) decides to run away and another decides to pursue, then we enter a chase scene. Chase scenes are handled by making an opposed check by the pursuer and the pursued. The check is a d20 roll + the character's (or monster's) run speed divided by 10 + DEX modifier.Whomever wins the opposed check gains his regular movement allowance of either widening the gap (if he's the pursued) or closing the gap (if he's the pursuer.)Let's have an example. A goblin pickpocket with a regular movement of 20 and DEX score of 14 would have a modifier of +10 (his run speed is 80, so his run modifier is 8, and his DEX modifier is +2.) If we assume he has the Run feat, his run speed would be 100, and his chase modifier would increase to +12. If this goblin attempts to pick the pocket of a human barbarian with a base movement of 40, he's in trouble if he gets caught, because the barbarian's chase modifier is +16 (we'll assume he has a DEX of 10--no modifier.)Clear as mud?After one minute (10 rounds) a character can no longer run without making a Constitution check. If he fails, he is fatigued, and follows all the rules for that condition.Attempting to throw off pursuit by ducking into an alley, losing oneself in a crowd, jumping over a barrier, knocking over stacked crates of fruit, etc. is where some GM adjudication comes in, but mostly it means making the appropriate skill check (Acrobatics, Sneak, etc.) and hoping that your opponent fails his associated roll (Acrobatics, Perception, etc.) Common sense rules here; because clever players can come up with many different actions, and because I can't predict what they may be, I make no attempt to make a comprehensive ruleset, merely to point to the skill system as the best way to translate most potential actions.If one member of a chase is mounted, obviously the mounts run speed is used, not the rider's, although he might need to make Ride checks as normal, especially if attempting anything tricky to keep up in the chase. If the chase scene takes place in unusual terrain, the GM can apply modifier as needed, or even require periodic Reflex saves or Acrobatics checks for runners to maintain their regular speed. Swimming, flying, or even burrowing chases obviously use the swim (or fly, or burrow) speed of the chase participant, but that's obvious, right?