Cosmological simulations of galaxy formation appear to show a" two-phase" character with a rapid early phase at z≳ 2 during which" in situ" stars are formed within the galaxy from infalling cold gas followed by an extended phase since z≲ 3 during which" ex situ" stars are primarily accreted. In the latter phase, massive systems grow considerably in mass and radius by accretion of smaller satellite stellar systems formed at quite early times (z> 3) outside of the virial radius of the forming central galaxy. These tentative conclusions are obtained from high-resolution re-simulations of 39 individual galaxies in a full cosmological context with present-day virial halo masses ranging from 7� 10 11 M☉ h− 1≲ M vir≲ 2.7� 10 13 M☉ h− 1 (h= 0.72) and central galaxy masses between 4.5� 10 10 M☉ h− 1≲ M*≲ 3.6� 10 11 M☉ h− 1. The simulations include the effects of a uniform UV background, radiative cooling, star formation, and energetic feedback from Type II supernova. The importance of stellar accretion increases with galaxy mass and toward lower redshift. In our simulations, lower mass galaxies (M*≲ 9� 10 10 M☉ h− 1) accrete about 60% of their present-day stellar mass. High-mass galaxy (M*≳ 1.7� 10 11 M☉ h− 1) assembly is dominated by accretion and merging with about 80% of the stars added by the present day. In general the simulated galaxies approximately double their mass since z= 1. For massive systems this mass growth is not accompanied by significant star formation. The majority of the in situ created stars are formed at z> 2, primarily out of cold gas flows. We recover the observational result of" archaeological downsizing," where the most massive galaxies harbor the oldest stars. We find that this is not in contradiction with hierarchical structure formation. Most stars in the massive galaxies are formed early on in smaller structures; the galaxies themselves are assembled late.