  Observations of intergalactic neutral hydrogen can provide a wealth of
information about structure and galaxy formation, potentially tracing accretion
and feedback processes on Mpc scales. Below a column density of NHI ~ 10^19
cm-2, the "edge" or typical observational limit for HI emission from galaxies,
simulations predict a cosmic web of extended emission and filamentary
structures. We study the distribution of neutral hydrogen and its 21cm emission
properties in a cosmological hydrodynamic simulation, to gain more insights
into the distribution of HI below NHI ~ 10^19 cm-2. Such Lyman Limit systems
are expected to trace out the cosmic web, and are relatively unexplored.
Beginning with a 32 h^-1 Mpc simulation, we extract the neutral hydrogen
component by determining the neutral fraction, including a post-processed
correction for self-shielding based on the thermal pressure. We take into
account molecular hydrogen, assuming an average density ratio Omega_H2 /
Omega_HI = 0.3 at z = 0. The statistical properties of the HI emission are
compared with observations, to assess the reliability of the simulation. The
simulated HI distribution robustly describes the full column density range
between NHI ~ 10^14 and NHI ~ 10^21 cm-2 and agrees very well with available
measurements from observations. Furthermore there is good correspondence in the
statistics when looking at the two-point correlation function and the HI mass
function. The reconstructed maps are used to simulate observations of existing
and future telescopes by adding noise and taking account of the sensitivity of
the telescopes. The general agreement in statistical properties of HI suggests
that neutral hydrogen as modeled in this hydrodynamic simulation is a fair
representation of that in the Universe. (abridged)
