We compute the z = 3 neutral hydrogen column density distribution function f(NHI) for 19 simulations drawn from the Overwhelmingly Large Simulations project using a post-processing correction for self-shielding calculated with full radiative transfer of the ionizing background radiation. We investigate how different physical processes and parameters affect the abundance of Lyman-limit systems (LLSs) and damped Lyman α absorbers including: (i) metal-line cooling; (ii) the efficiency of feedback from supernovae and active galactic nuclei; (iii) the effective equation of state for the interstellar medium; (iv) cosmological parameters; (v) the assumed star formation law and (vi) the timing of hydrogen reionization. We find that the normalization and slope, D = d log _{10} f /d log _{10} N_{H I}, 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 per cent to f(NHI) in the LLS column density range. At higher column densities, variations in f(NHI) become larger (approximately 0.5 dex at f(NHI) = 1022 cm-2 and 1.0 dex at f(NHI) = 1022 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. Tools to reproduce all figures in this work can be found at the following url: https://bitbucket.org/galtay/hi-cddf-owls-1