Abstract
The emerging empirical picture of galaxy stellar mass (M_s) assembly shows that galaxy population buildup proceeds from top to down in M_s. By connecting galaxies to ΛCDM halos and their histories, individual (average) M_s growth tracks can be inferred. These tracks show that massive galaxies assembled their M_s the earlier the more massive the halo, and that less massive galaxies are yet actively growing in M_s, the more active the less massive is the halo. The predicted star formation rates as a function of mass and the downsizing of the typical mass that separate active galaxies from the passive ones agree with direct observational determinations. This implies that the ΛCDM scenario is consistent with these observations. The challenge remains in explaining how the M_s assembly (downsizing) systematically shifts from the corresponding halo mass assembly (upsizing).
