  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.
