  We study the high column density regime of the HI column density distribution
function and argue that there are two distinct features: a turnover at NHI ~
10^21 cm^-2 which is present at both z=0 and z ~ 3, and a lack of systems above
NHI ~ 10^22 cm^-2 at z=0. Using observations of the column density
distribution, we argue that the HI-H2 transition does not cause the turnover at
NHI ~ 10^21 cm^-2, but can plausibly explain the turnover at NHI > 10^22 cm^-2.
We compute the HI column density distribution of individual galaxies in the
THINGS sample and show that the turnover column density depends only weakly on
metallicity. Furthermore, we show that the column density distribution of
galaxies, corrected for inclination, is insensitive to the resolution of the HI
map or to averaging in radial shells. Our results indicate that the similarity
of HI column density distributions at z=3 and z=0 is due to the similarity of
the maximum HI surface densities of high-z and low-z disks, set presumably by
universal processes that shape properties of the gaseous disks of galaxies.
Using fully cosmological simulations, we explore other candidate physical
mechanisms that could produce a turnover in the column density distribution. We
show that while turbulence within GMCs cannot affect the DLA column density
distribution, stellar feedback can affect it significantly if the feedback is
sufficiently effective in removing gas from the central 2-3 kpc of
high-redshift galaxies. Finally, we argue that it is meaningful to compare
column densities averaged over ~ kpc scales with those estimated from quasar
spectra which probe sub-pc scales due to the steep power spectrum of HI column
density fluctuations observed in nearby galaxies.
