Ok I will put in some of my gaming experiences with AI in Dom II in order to quench everyone’s fears, and even compare to AOW2 AI since it can be used as example of All-Seeing AI (although I don't like doing that).
First let me point out something, AI has all the info of your empire simply because it's stored in your PC.
The difference about all-seeing and not all-seeing AI is what info he will use when he makes his turn; will he use info that would be available to human player only or more than that. More than that can be only little more and only in specific areas of the game, not necessarily everything.
My experience with AI in Dom II is quite different from Jaque's in Dom I. Lets stick with seeking arrows for now. AI in my games uses them a lot; hell most AI's with powerful air magic seem to go after me as soon as they spot me so I've seen a lot of arrows land on my provinces.
I'll concentrate on one specific game where I was fighting Vanheim (I was Man) on large map with both of us quite large and only at war with each other. As soon as Vanheim declared war on me he started using those arrows and he didn't stop until I took his home province and most of his other provinces. During this pretty long fight (both of us had quite stretched empires and lots of resources) he would use seeking arrows in what can safely called random fashion. I had Groups of mages in couple of my inner provinces making items and researching (lots of sages particularly in couple of provinces). Also, logically, I had a number of good commanders doing war with at the front and lots of priests along borders to prevent enemy domains speeding into my provinces (1 or 2 at each border province at least). The arrows that AI sent against my troops would mostly hit my most numerous commander types along the borders - priests. Sage never got hit as I had 20-30 provinces and they were only in 2-3 of them so I guess they got lucky. Sometimes some of my commanders would get hit too and more powerful mages but such events would be something like 1 in 3 or 4 arrows. AI wouldn't target same provinces all the time nor did he ever displayed awareness that he knew where my most powerful commanders are, including my pretender (Cyclops in that case). So I draw 2 conclusions from this experience:
1) AI did not use info on my commanders locations (did not see them if you will) and did not target my most powerful ones with ranged spells, instead using ranged spells in semi-random fashion (semi because he would target my border provinces mostly, although not exclusively).
2) During my game fighting with Vanheim I did get the feeling AI knows what provinces I own.
Ok, getting this cleared lets comment scouting for a moment. In Dom II I kill hordes of black servants (these seem to be most numerous), spy's, scouts and assassins that other empires send through my borders. He does that very often and apparently builds scouting units and sends them around. So, if AI builds them and sends them roaming around (and assassinating some of your commanders in the process - yes I had such experiences too and they were not random events but one specific Abyssian assassin that killed 2 of my priests and 1 not so weak mage) and knows where your borders are, can you really call him cheating? If he builds and sends scouts around, then its logical he will be allowed to know where your provinces are located since that is the info they would gather.
In all my games so far (and I've had a lots of them by now) I have NEVER felt like AI is truly cheating, although I never played on levels harder then normal either. On normal level, IIRC AI has same conditions player has (no special bonuses) and it really FEELS like you are playing on even terms instead of being cheated.
You know how AI in AOW2 knows where you cities, your sites and your armies are (pretty much everything)? So when you move defenders from one city on remote side of the map, he will send force to capture that town. And if you put defenders back in that town he will pull back his now (in his, not so good, judgment) insufficient force even if there is no way he could normally see it. In AOW2 AI would react to all events around showing that he has access to all the info normal player would not. That is safe to say that it's cheating.
OTOH in Dom II I have never seen such AI behavior. AI does not favor provinces with lots of special sites (discovered or not) and does not attack as if he knows where your main castle is. He will focus on fortifications in your empire since they are strategically valuable and will favor your home province but only when he reaches them. He won't send a force from other side of the map to capture your weakly defended home province like AOW AI would do.
Ok, to wrap this up, AI in Dominions II is simply playing like normal human player would (of course, not as strong as experienced Dom veteran can, but that is why stronger levels are available) and in ALL my games I have never felt cheated by AI.
I hope this will quench some of your fears regarding this matter.
BTW. This post could very well be my largest so far.