(This question is made with modern Fallout (3+) in mind, but feel free to answer about classic Fallout if the question makes sense in that context.)

One thing I have been wondering: How active is the AI in areas that you are not in? For example, can a fight break out when you are on the opposite side of the map? Alternatively, if you are in an area where a fight breaks out (without you being involved), and you fast travel before the fight resolves, will the fight continue to play out (possibly with casualties) by the time you get back?

I know that, in Wasteland (the precursor to Fallout), the AI would not operate in areas you aren't in, but timers would still run (so that an injured character's condition would worsen, for example).

Obviously won't happen, unless a timer is running because of a quest.
The reason is: memory consumption. And in Fallout 3+ the whole thing is "open world", thus would not make sense anyway.

Unless youask wether there canbe in F3+ similar things as in classic Fallouts: X vs Y monsters random encounter. Still won't happen whenyou're not in the vicinity, that's for sure, but wether it can happen at all...

I would think the reason would be CPU rather than memory consumption; to my understanding, graphics are the one thing that consumes the most memory in these type of games.

In any case, how far away does the AI operate anyway? For example, does it stop as soon as you leave the area, or does it continue until you go sufficiently far away, or until a certain amount of time passes?

I note that, in Oblivion, NPCs can sometimes travel between cells (like entering and leaving a building); does this happen here, and if so, is that simulated when you aren't in the area? If not, how does the game decide where to place the character when you re-enter the area?

I believe the locations of NPCs are determined based on the scripting - which I guess could be considered their "AI". At their most basic, a script just places a character in the same place every time you go there.

Many scripts use time of day to determine where characters go - or at least, where they start when you get there. If a character needs to react to some event (e.g. you destroying a location, completing a specific mission, etc.), then additional variables would be checked - e.g. lots of characters in Tenpenny Tower change depending on how you resolved the Tenpenny Towers ghoul situation, but these don't take effect until a few days after you've completed a certain quest.

As far as I'm aware, the characters don't move (nor are "simulated") beyond a certain range from the player In F3/NV. There aren't many games that do this - the only one I can think of would be Space Rangers 2/HD.

As for what that range actually is - I have no idea. It's range is probably larger than your "visual" range in-game, but I have no idea exactly how much larger.

thanks for the advice