We examine the growth of the stellar content of galaxies from z=3-0 in cosmological hydrodynamic simulations incorporating parameterised galactic outflows. Without outflows, galaxies overproduce stellar masses (M*) and star formation rates (SFRs) compared to observations. Winds introduce a three-tier form for the galaxy stellar mass and star formation rate functions, where the middle tier depends on differential (i.e. mass-dependent) recycling of ejected wind material back into galaxies. A tight M*-SFR relation is a generic outcome of all these simulations, and its evolution is well-described as being powered by cold accretion, although current observations at z>2 suggest that star formation in small early galaxies must be highly suppressed. Roughly one-third of z=0 galaxies at masses below M^* are satellites, and star formation in satellites is not much burstier than in centrals. All models fail to suppress star formation and stellar mass growth in massive galaxies at z<2, indicating the need for an external quenching mechanism such as black hole feedback. All models also fail to produce dwarfs as young and rapidly star-forming as observed. An outflow model following scalings expected for momentum-driven winds broadly matches observed galaxy evolution around M^* from z=0-3, which is a significant success since these galaxies dominate cosmic star formation, but the failures at higher and lower masses highlight the challenges still faced by this class of models. We argue that central star-forming galaxies are well-described as living in a slowly-evolving equilibrium between inflows from gravity and recycled winds, star formation, and strong and ubiquitous outflows that regulate how much inflow forms into stars. Star-forming galaxy evolution is thus primarily governed by the continual cycling of baryons between galaxies and intergalactic gas.
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