At high redshifts, the observed galaxy mass functions are fit reasonably well by a Schecter function, having an exponential falloff on the high mass end, much like the mass functions for low-z galaxies. This is in stark contrast to the IR luminosity function which traces star formation activity is best fit with a power-law falloff at high luminosities. In this contribution, I review the characteristics of galactic scale star formation in low redshift galaxies, arguing for two modes: a quiescent mode which depends linearly on the mass of molecular gas and a dynamically driven starburst mode exemplified by merging ULIRG systems. I then summarize recent analysis from the COSMOS survey relating to the cosmic evolution of the galaxy merger rate. This analysis shows the number of close galaxy pairs dramatically increasing as (1+z)^(2.5) at z = 0.2 – 1.2, indicating strong evolution in the galaxy merger rate. This cosmic evolution is similar to that derived for the dark matter (DM) halos in ΛCDM simulations. With this evolution of the galaxy merger rate, I have modeled the galaxy mass and star-formation luminosity functions in a Monte Carlo simulation starting from z = 6. The simulation is initiated with a galaxy mass function similar to that of the expected DM halos at z = 6, scaled down by the cosmic baryon/DM ratio, with 90% of the baryons being in the gas and 10% in stars. We let the galaxies evolve – converting gas into stars via the quiescent and starburst modes of star formation, the latter triggered by galaxy-galaxy merging. In order to avoid exhaustion of the initial gas supply, it becomes clear that gas accretion from the large scale structure environment is required; otherwise the ISM contents of galaxies are far too low already by z ~3. In this model, the power-law high L end of the SF luminosity function is the result of the merger-induced SB activity.