OK, here are the changes Ive introduced in the new version (and that Afforess will hopefully include in his latest A.N.D.):
Units can still claim any enemy or neutral tiles. However, if your civ doesnt have culture in a claimed tile, you must keep at least one unit on it each turn in order not to lose it again (i.e. if you claim tiles far from your cities, you must keep forces there to keep them). For instance, if you capture and raze a city and move the units away, youll lose all the tiles that the city provided.
For each tile, theres a new info on mouse hover, saying Owner: CivX, because now the owner may be the one that doesnt have the most culture in it (there are no more 10000000 culture points for claiming tiles; culture remains the same, but the real owner is decided based on claiming first, and then the culture).
Forts as Cities:
This component has grown into an independent mod and can be used even without fixed borders.
The point is that all forts (and other fort-like improvements*) really act as cities when it comes to culture and borders. They emit a minimal amount of culture in their adjacent tiles, thus enabling you to have additional territory without units far from cities, as long as you keep the forts under your control. You dont even need units inside forts, but its like leaving a city unguarded. Once forts are captured (in war, like cities), they give the new owner the control of the surrounding tiles. There are some additional rules when a fort shares adjacent tile with a city then the city is the main owner of the tile and you must capture the city itself in order to get the adjacent tile (but the fort you get as soon as you capture it).
* Fort-like improvements are the ones defined in CIV4ImprovementInfos.xml with bActsAsCity=1 (old BtS tag, I havent introduced it).
Influence Driven War:
IDW has been slightly altered to support fixed borders and forts as cities. If the losing unit's owner has fixed borders, the tiles can't lose the last point of culture from culture transfer. Also, if a tile has a fort (owner doesn't have to have fixed borders), that tile can't lose the last point of culture. All other culture points (up to the last one) can be transferred and will affect the cities' nationality (if battles take place close to cities).
Finally, AI has been improved in 2 ways:
1. it has learned to build forts outside its borders (giving high priority to far away resources). The old AI then knows to guard those forts with units.
2. claiming of tiles has been improved drastically, AI will try to claim tiles as it advances into enemy territory toward cities.