It depends from campaign to campaign. There are several scripted wars:
1. Maratha - Mughal, that start out at war.
2. Ottomans - Russia, that start out at war.
3. Sweden vs. Russia-Denmark-Poland & Lithuania. Seems to start on turn 2 most of the time.
4. Prussia vs. Austria (depends on #5 taking place).
5. Prussia vs. Poland & Lithuana (depends on #4 taking place).
6. GB & UP vs. Spain & France (random turn).
7. Austria, Bavaria & Wurtemburg vs. France (random turn)

Prussia almost always gets its rear whipped. I have seen posts where people have talked about the AI Prussia expanding. I've seen Prussia take at most two regions, then get embroiled on a multi-front war and lose.

The Ottoman-Russian war rarely progresses. The Ottoman AI builds fleets like crazy, and the Russian AI can be pre-occupied with Crimea, Sweden or Gergia, depending on how its wars are going.

I've seen UP take and then lose Flanders in a turn. I've seen France destroyed by a combination of Wurtemburg + myself. Spain doesn't have enough troops in Flanders to mount a decent attack.

The four most expansionist major nations I have seen in my games so far are: Marathas & Mughals - one wins, the other dies, Sweden and Russia.