I assume when you say dispersed you mean camping at a place other than an established campground. Is that correct?
If it is then you are in luck. You can camp anywhere in the Whites as long as you are from 200 feet to .25 mile away from waterways and certain trails. You also are not allowed to camp within .25 mile of an established campground and you can't camp above treeline except in the winter under certain conditions. They don't like to see (or catch you) cutting trees but grabbing deadfall is no problem. That really leaves lots of places to camp in an area almost the size of Rhode Island.
White mountain backcountry camping rules
Most of the places they require you to be at least .25 miles away from you will want to be anyway. The reason that rule is in place is because that area gets such heavy use. You will need a map of the forest for these areas to be known to you. If you have any questions feel free to ask. I do lots of camping and hiking in the Whites and have for 20 years. I have also worked with some of the SAR units and other rescue units in the area.
KR