Under the new system, you need one lord and one knight per region to run an acceptable tax. Since rulers, dukes, etc. can all be knights as well (though only of their own duchies/regions), that means 2 characters per region the realm holds. 3-4 if you want to run at 100% efficiency.
Frankly, if your realm has less than 2-3 characters per region, it is trying to hold more land than it can and should get rid of a region or two.