We use hydrodynamical simulations from the OverWhelmingly Large Simulations project to investigate the dependence of the physical properties of galaxy populations at redshift 2 on the assumed star formation law, the equation of state imposed on the unresolved interstellar medium, the stellar initial mass function, the reionization history and the assumed cosmology. This work complements that of Paper I, where we studied the effects of varying models for galactic winds driven by star formation and active galactic nucleus. The normalization of the matter power spectrum strongly affects the galaxy mass function, but has a relatively small effect on the physical properties of galaxies residing in haloes of a fixed mass. Reionization suppresses the stellar masses and gas fractions of low-mass galaxies, but by z = 2 the results are insensitive to the timing of reionization. The stellar initial mass function mainly determines the physical properties of galaxies through its effect on the efficiency of the feedback, while changes in the recycled mass and metal fractions play a smaller role. If we use a recipe for star formation that reproduces the observed star formation law independently of the assumed equation of state of the unresolved interstellar medium, then the latter is unimportant. The star formation law, i.e. the gas consumption time-scale as a function of surface density, determines the mass of dense, star-forming gas in galaxies, but affects neither the star formation rate nor the stellar mass. This can be understood in terms of self-regulation: the gas fraction adjusts until the outflow rate balances the inflow rate.