We study the density profiles of collapsed galaxy-size dark matter halos with masses 10 super(11) to 5 x 10 super(12) M sub( )focusing mostly on the halo outer regions from the formal virial radius R sub(vir) up to 5R sub(vir)-7R sub(vir). We find that isolated halos in this mass range extend well beyond R sub(vir) exhibiting all properties of virialized objects up to 2R sub(vir)-3R sub(vir): relatively smooth density profiles and no systematic infall velocities. The dark matter halos in this mass range do not grow as one naively may expect through a steady accretion of satellites; i.e., on average there is no mass infall. This is strikingly different from more massive halos, which have large infall velocities outside the virial radius. We provide an accurate fit for the density profile of these isolated galaxy-size halos. For a wide range 0.01 R sub(vir)-2R sub(vir) of radii the halo density profiles are fitted with the approximation P = P sub(s) exp -2n (x super(1/n) - 1) + < P sub(m) >, where x = r/r sub(s),< P sub(m) > is the mean matter density of the universe, and the index n is in the range n = 6-7.5. These profiles do not show a sudden change of behavior beyond the virial radius. For larger radii we combine the statistics of the initial fluctuations with the spherical collapse model to obtain predictions for the mean and most probable density profiles for halos of several masses. The model gives excellent results beyond 2-3 formal virial radii for the most probable profile and qualitatively correct predictions for the mean profile.