We investigate the column density distribution function of neutral hydrogen at redshift z = 3 using a cosmological simulation of galaxy formation from the OverWhelmingly Large Simulations project. The base simulation includes gravity, hydrodynamics, star formation, supernovae feedback, stellar winds, chemodynamics, and element-by-element cooling in the presence of a uniform UV background. Self-shielding and formation of molecular hydrogen are treated in post-processing, without introducing any free parameters, using an accurate reverse ray-tracing algorithm and an empirical relation between gas pressure and molecular mass fraction. The simulation reproduces the observed z = 3 abundance of Lyα forest, Lyman limit, and damped Lyα H I absorption systems probed by quasar sight lines over 10 orders of magnitude in column density. Self-shielding flattens the column density distribution for N H I > 1018 cm-2, while the transition to fully neutral gas and conversion of H I to H2 steepen it around column densities of N H I = 1020.3 cm-2 and N H I = 1021.5 cm-2, respectively.