  It is often assumed that local sources of ionizing radiation have little
impact on the distribution of HI in the post-reionization Universe. While this
is a good assumption for the IGM, analytic arguments suggest that local sources
may typically be more important than the background radiation for high column
density absorbers (N_HI > 10^17 /cm^2). We post-process cosmological
simulations with accurate radiation transport to investigate the impact of
local stellar sources on the HI distribution. We demonstrate that the limited
numerical resolution and the simplified treatment of the ISM that are typical
of current cosmological simulations provide significant challenges, but that
many of the problems can be overcome by taking two steps. First, using ISM
particles rather than stellar particles as sources results in a much better
sampling of the source distribution. Second, by rescaling the source
luminosities so that the amount of radiation escaping into the IGM agrees with
that required to produce the observed background, many of the results become
insensitive to errors in the predicted fraction of the radiation that escapes
the immediate vicinity of the sources. By adopting this strategy and by varying
the assumptions about the structure of the unresolved ISM, we conclude that we
can robustly estimate the effect of local sources for column densities N_HI <<
10^21 /cm^2. However, neither the escape fraction of ionizing radiation nor the
effect of local sources on the abundance of N_HI >~ 10^21 systems can be
predicted with confidence. We find that local stellar radiation is unimportant
for N_HI << 10^17, but that it can affect Lyman Limit and DLA systems. For
10^18 < N_HI < 10^21 the impact of local sources increases with redshift. At z
= 5 the abundance of absorbers with N_HI >> 10^17 is substantially reduced, but
at z = 0 the reduction only becomes significant for N_HI >~ 10^21 /cm^2.
