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 intrinsic 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 \mathrm { kpc } for GRBs compared with 4 \mathrm { kpc } for QSO-DLAs . However , an equally important difference is that GRB-DLAs are predominantly associated with halos of mass 10 ^ { 10 } < M _ { \mathrm { vir } } / M _ { \odot } < 10 ^ { 12 } , an order of magnitude larger than the hosts of QSO-DLAs . Accordingly , there are differences in the stellar properties of hosts . For instance mean star formation rates are higher : \langle \dot { M } _ { \star } \rangle \simeq 10 \mathrm { M } _ { \odot } \mathrm { yr } ^ { -1 } for GRB-DLAs compared with \langle \dot { M } _ { \star } \rangle \simeq 1 \mathrm { M } _ { \odot } \mathrm { yr } ^ { -1 } for QSO-DLAs . Our simulations accurately predict the form of the GRB-DLA H i column density distribution , producing quantitative agreement for N _ { \mathrm { HI } } > 10 ^ { 19 } { cm } ^ { -2 } , but they somewhat underpredict the incidence of low column densities N _ { \mathrm { HI } } < 10 ^ { 19 } { cm } ^ { -2 } . This is reflected in our estimate of the ionizing photon escape fraction , f _ { \mathrm { esc } } \simeq 1 \% , which is lower than the observational GRB-derived escape fraction ( 2 \% ) . Line-of-sight neutral gas metallicities predicted by our simulations ( 10 ^ { -2 } < Z / Z _ { \odot } < 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 _ { \odot } / 3 ) , confounding claims that the observed metallicity of GRB-DLAs poses a severe challenge to current GRB models .