We use hydrodynamic cosmological simulations to study damped Lyman-alpha (DLA) and Lyman limit (LL) absorption at redshifts z=2-4 in five variants of the cold dark matter scenario. Our standard simulations resolve the formation of dense concentrations of neutral gas in halos with circular velocity v_c roughly 140 km/s for Omega_m=1 and 90 km/s for Omega_m=0.4, at z=2; an additional LCDM simulation resolves halos down to v_c approximately 50 km/s at z=3. We find a clear relation between HI column density and projected distance to the center of the nearest galaxy, with DLA absorption usually confined to galactocentric radii less than 10-15 kpc and LL absorption arising out to projected separations of 30 kpc or more. Detailed examination provides evidence of non-equilibrium effects on absorption cross-section. If we consider only absorption in the halos resolved by our standard simulations, then all five models fall short of reproducing the observed abundance of DLA and LL systems at these redshifts. If we extrapolate to lower halo masses, we find all four models are consistent with the observed abundance of DLA systems if the the extrapolated behavior extends to circular velocities roughly 50-80 km/s, and they may produce too much absorption if the relation continues to 40 km/s. Our results suggest that LL absorption is closely akin to DLA absorption, arising in less massive halos or at larger galactocentric radii but not caused by processes acting on a radically different mass scale.
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