We combine cosmological, hydrodynamical simulations with accurate radiative
transfer corrections to investigate the relation between strong HI absorbers
(N_HI >~ 10^17 /cm^2) and galaxies at redshift z = 3. We find a strong
anti-correlation between the column density and the impact parameter that
connects the absorber to the nearest galaxy. The median impact parameters for
Lyman Limit (LL) and Damped Lyman-{\alpha} (DLA) systems are ~10 and ~1 proper
kpc, respectively. If normalized to the size of the halo of the nearest central
galaxy, the median impact parameters for LL and DLA systems become ~1 and
~10^-1 virial radii, respectively. At a given HI column density, the impact
parameter increases with the mass of the closest galaxy, in agreement with
observations. We predict most strong HI absorbers to be most closely associated
with extremely low-mass galaxies, M_star < 10^8 M_sun and star formation rate
<10^-1 M_sun/yr. We also find a correlation between the column density of
absorbers and the mass of the nearest galaxy. This correlation is most
pronounced for DLAs with N_HI > 10^21 /cm^2 which are typically close to
galaxies with M_star >~ 10^9 M_sun. Similar correlations exist between column
density and other properties of the associated galaxies such as their star
formation rates, halo masses and HI content. The galaxies nearest to HI
absorbers are typically far too faint to be detectable with current
instrumentation, which is consistent with the high rate of (often unpublished)
non-detections in observational searches for the galaxy counterparts of strong
HI absorbers. Moreover, we predict that the detected nearby galaxies are
typically not the galaxies that are most closely associated with the absorbers,
thus causing the impact parameters, star formation rates and stellar masses of
the observed counterparts to be biased high.Comment: 21 pages, 14 figures; Accepted for publication in MNRA