We compute the z = 3 neutral hydrogen column density distribution function f(NHI) for 19 simulations drawn from the OWLS project using a post-processing correction for self-shielding calculated with full radiative transfer of the ionising background radiation. We investigate how different physical processes and parameters affect the abundance of Lyman-limit systems (LLSs) and damped Lyman-alpha absorbers (DLAs) including: i) metal-line cooling; ii) the efficiency of feedback from SNe and AGN; iii) the effective equation of state for the ISM; iv) cosmological parameters; v) the assumed star formation law and; vi) the timing of hydrogen reionization . We find that the normalisation and slope, D = d log10 f /d log10 NHI, of f(NHI) in the LLS regime are robust to changes in these physical processes. Among physically plausible models, f(NHI) varies by less than 0.2 dex and D varies by less than 0.18 for LLSs. This is primarily due to the fact that these uncertain physical processes mostly affect star-forming gas which contributes less than 10% to f(NHI) in the the LLS column density range. At higher column densities, variations in f(NHI) become larger (approximately 0.5 dex at NHI = 10^22 cm^-2 and 1.0 dex at NHI = 10^23 cm^-2) and molecular hydrogen formation also becomes important. Many of these changes can be explained in the context of self-regulated star formation in which the amount of star forming gas in a galaxy will adjust such that outflows driven by feedback balance inflows due to accretion. Data and code to reproduce all figures can be found at the following url: https://bitbucket.org/galtay/hi-cddf-owls-1
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