Many rumors grow steam, get debunked, and fade away. One rumor about the admission process at UVa never goes away: the rumor about regional quotas.
There is one quota that affects the admission process at UVa. The Commonwealth of Virginia mandates that 2/3 of the students at the University be Virginia residents. Beyond that, there are no quotas with respect to regions, counties, or high schools. There are trends in the population here, of course. Densely populated areas of the state tend to have many high schools and send many students to UVa.
Obviously, most admission offices want to bring in an interesting class that has people from many backgrounds, but we have not been handed target numbers for different regions, counties, or populations beyond that 2/3 : 1/3 ratio.
If you want to see admission statistics by residency, check out this chart on the Office of Institutional Assessment's website.