Cosmological simulations of galaxy formation appear to show a ’ two-phase ’ character with a rapid early phase at z \gtrsim 2 during which ’ in-situ ’ stars are formed within the galaxy from infalling cold gas followed by an extended phase since z \lesssim 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 \times 10 ^ { 11 } M _ { \odot } h ^ { -1 } \lesssim M _ { \mathrm { vir } } \lesssim 2.7 \times 10 ^ { 13 } M _ { \odot } h ^ { -1 } ( h=0.72 ) and central galaxy masses between 4.5 \times 10 ^ { 10 } M _ { \odot } h ^ { -1 } \lesssim M _ { * } \lesssim 3.6 \times 10 ^ { 11 } M _ { % \odot } h ^ { -1 } . The simulations include the effects of a uniform UV background , radiative cooling , star formation and energetic feedback from SNII . The importance of stellar accretion increases with galaxy mass and towards lower redshift . In our simulations lower mass galaxies ( M _ { * } \lesssim 9 \times 10 ^ { 10 } M _ { \odot } h ^ { -1 } ) accrete about 60 per cent of their present-day stellar mass . High mass galaxy ( M _ { * } \gtrsim 1.7 \times 10 ^ { 11 } M _ { \odot } h ^ { -1 } ) assembly is dominated by accretion and merging with about 80 per cent 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 is 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 .