We investigate the properties of damped Ly{alpha} absorption systems (DLAs) in semi-analytic models of galaxy formation, including partitioning of cold gas in galactic discs into atomic, molecular, and ionized phases with a molecular gas-based star formation recipe. We investigate two approaches for partitioning gas into these constituents: a pressure-based and a metallicity-based recipe. We identify DLAs by passing lines of sight through our simulations to compute HI column densities. We find that models with standard gas radial profiles - where the average specific angular momentum of the gas disc is equal to that of the host dark matter halo - fail to reproduce the observed column density distribution of DLAs. These models also fail to reproduce the distribution of velocity widths {Delta}v, overproducing low {Delta}v relative to high {Delta}v systems. Models with extended radial gas profiles - corresponding to gas discs with higher specific angular momentum - are able to reproduce quite well the column density distribution of absorbers over the column density range 19 < log NHI < 22.5 in the redshift range 2 < z < 3.5. The model with pressure-based gas partitioning also reproduces the observed line density of DLAs, HI gas density, and {Delta}v distribution at z < 3 remarkably well. However all of the models investigated here underproduce DLAs and the HI gas density at z > 3. If this is the case, the flatness in the number of DLAs and HI gas density over the redshift interval 0 < z < 5 may be due to a cosmic coincidence where the majority of DLAs at z > 3 arise from intergalactic gas in filaments while those at z < 3 arise predominantly in galactic discs. We further investigate the dependence of DLA metallicity on redshift and {Delta}v, and find reasonably good agreement with the observations, particularly when including the effects of metallicity gradients (abbrv.).
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