  We calculate the distribution of HI within 750 proper kpc/h of a quasar, Lbol
= 1.62e13 Lsun, powered by an SMBH, Mbh = 4.47e8 Msun, at z = 3. Our numerical
model includes a cosmological hydrodynamic simulation that tracks the self
consistent growth and thermal feedback of black holes calculated using GADGET-3
as well as a detailed post-processing ray tracing treatment of the non-uniform
ionizing radiation field calculated using SPHRAY, which naturally accounts for
the self shielding of optically thick systems. We show that the correct
treatment of self shielding introduces a flattening feature into the neutral
column density distribution around Log NHI = 20 and that regions with the
lowest neutral fractions are not those with the highest density gas. For
comparison, we solve a Ricatti equation which determines the equilibrium
Hydrogen ionization fractions in the presence of a radiation field that falls
off as 1/r^2 with regions above a given gas density threshold completely
shielded from ionizing radiation. We demonstrate that these semi analytic
models cannot reproduce the HI field calculated using SPHRAY. We conclude by
comparing our models of this single proximity zone to observations by Hennawi
and Prochaska of the absorption spectra of background quasars which are
coincident on the sky with foreground quasars in their Quasars Probing Quasars
(QPQ) series of papers. Compared to the QPQ sample, we find a factor of 3 fewer
optically thick (Log NHI > 17.2) systems around our quasar, however the dark
matter halo that hosts our simulated quasar, Mhalo = 5.25e12 Msun, is less
massive than the typical QPQ host halo by a factor of four. Allowing for a
linear scaling between halo mass, baryonic overdensity and number of absorbers,
we estimate the typical host halo mass in the QPQ sample as 1.92e13 Msun.
