  In recent work, we have shown that it is possible to link quantitatively many
aspects of damped Lyman alpha (DLA) absorbers in the spectra of quasars to high
resolution simulations of galaxy formation. Using runs from the same series of
hydrodynamic numerical studies, we consider the expected properties of Lyman
alpha absorbers seen in the spectra of high redshift (z>2) gamma ray burst
afterglows (GRB-DLAs). If GRBs are associated with the death of massive stars,
their afterglows provide insights into otherwise unprobed regions of
protogalactic objects, but detailed physical interpretations are currently
embryonic.
  We find that median impact parameters (measured from the potential minimum)
are approximately 1 kpc for GRBs compared with 4 kpc for QSO-DLAs. However, an
equally important difference is that GRB-DLAs are predominantly associated with
halos of mass 10^10<M_vir/M_sol<10^12, an order of magnitude larger than the
hosts of QSO-DLAs. Accordingly, there are differences in the stellar properties
of hosts.
  Our simulations accurately predict the form of the GRB-DLA HI column density
distribution, producing quantitative agreement for N_HI>10^19 cm^-2, but they
somewhat underpredict the incidence of low column densities N_HI<10^19 cm^-2.
Line-of-sight neutral gas metallicities predicted by our simulations (10^-2 <
Z/Z_sol < 1) are consistent with the modest observational constraints. Because
of large internal dispersions in gas metallicities, this agreement is not
significantly compromised by imposing a cut-off on the metallicity of stars
able to launch GRBs (Z_star<Z_sol/3), confounding claims that the observed
metallicity of GRB-DLAs poses a challenge to current GRB models. (Abridged.)
