You mean the fewest DOW's possible. In that case, 1. The eleven are all vassals, and two of the 3 powers have a defensive pact. The one left out DOW's on one of the other 2, thus pulling the third one in via the defensive pact. The eleven other vassals are also pulled in because of their masters.
If you don't mean minimal DOWs, then there could be as many as, let's see, not good at math on Saturday mornings, I think 92? If every one was independent, with no pacts, no alliences, and every one declared war on every other person, it would be 196. Take out the ones that would already have been declared war on, and I get 92.
I guese you could have any where in between 1 and 92, if you factor in different amounts of vassals/pacts/alliances.
EDIT: Wait, would it count as a seperate DOW if it was because of a Defensive pact? If that counts as two DOWs, I would need to change it to 2 for my first scenario. Civs 4-14 are vassals to Civs 1-3. Civs 1 and 2 have a definsive pact, and Civ 3 DOWs on Civ 1, Civ 2 would be pulled in. Does Civ 2 Count as a DOW? Do all the vassals getting in on the war count as a DOW? If so, disregard any of my mindless babblings, that I hope count as a cohearent answer.