We present a robust method to constrain average galaxy star formation rates, star formation histories, and the intracluster light as a function of halo mass. Our results are consistent with observed galaxy stellar mass functions, specific star formation rates, and cosmic star formation rates from z=0 to z=8. We consider the effects of a wide range of uncertainties on our results, including those affecting stellar masses, star formation rates, and the halo mass function at the heart of our analysis. As they are relevant to our method, we also present new calibrations of the dark matter halo mass function, halo mass accretion histories, and halo-subhalo merger rates out to z=8. We also provide new compilations of cosmic and specific star formation rates; more recent measurements are now consistent with the buildup of the cosmic stellar mass density at all redshifts. Implications of our work include: halos near 10^12 Msun are the most efficient at forming stars at all redshifts, the baryon conversion efficiency of massive halos drops markedly after z ~ 2.5 (consistent with theories of cold-mode accretion), the ICL for massive galaxies is expected to be significant out to at least z ~ 1-1.5, and dwarf galaxies at low redshifts have higher stellar mass to halo mass ratios than previous expectations and form later than in most theoretical models. Finally, we provide new fitting formulae for star formation histories that are more accurate than the standard declining tau model. Our approach places a wide variety of observations relating to the star formation history of galaxies into a self-consistent framework based on the modern understanding of structure formation in LCDM. Constraints on the stellar mass-halo mass relationship and star formation rates are available for download at http://www.peterbehroozi.com/data.html .
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