Two of the dominant channels for galaxy mass assembly are cold flows (cold gas supplied via the filaments of the cosmic web) and mergers. How these processes combine in a cosmological setting, at both low and high redshift, to produce the whole zoo of galaxies we observe is largely unknown. Indeed there is still much to understand about the detailed physics of each process in isolation. While these formation channels have been studied using hydrodynamical simulations, here we study their impact on gas properties and star formation (SF) with some of the first from simulations that capture the multiphase, cloudy nature of the interstellar medium (ISM), by virtue of their high spatial resolution (and corresponding low temperature threshold). In this regime, we examine the competition between cold flows and a supernovae(SNe)-driven outflow in a very high-redshift galaxy (z ≈ 9) and study the evolution of equal-mass galaxy mergers at low and high redshift, focusing on the induced SF. We find that SNe-driven outflows cannot reduce the cold accretion at z ≈ 9 and that SF is actually enhanced due to the ensuing metal enrichment. We demonstrate how several recent observational results on galaxy populations (e.g. enhanced HCN/CO ratios in ULIRGs, a separate Kennicutt Schmidt (KS) sequence for starbursts and the population of compact early type galaxies (ETGs) at high redshift) can be explained with mechanisms captured in galaxy merger simulations, provided that the multiphase nature of the ISM is resolved.