There may not be quotas among hs, but they will look for a balance across the state, both to be fair and to be geographically diverse within the state. The sheer number admitted from TJ does present a challenge. And because UVa is so very desirable, a lot of very top kids will apply. It’s one of the colleges I consider most unpredictable.
By all means, go for it. It’s one of my fav schools. But be aware.