A simple, 1-equation, galaxy formation model is applied to both the halo merger tree derived from a high-resolution dissipationless cosmological simulation and to 1/4 million Monte-Carlo halo merger trees. The galaxy formation model involves a sharp entropy barrier against the accretion of gas onto low-mass halos, the shock heating of infalling gas far from the central regions of massive halos, and supernova feedback that drives the gas out of shallow halo potential wells. With the first approach, we show that the large majority of galaxies within group- and cluster-mass halos, known to be mainly dwarf ellipticals, have acquired the bulk of their stellar mass through gas accretion and not via galaxy mergers. With the second approach, we qualitatively reproduce the downsizing trend of greater ages at greater masses in stars and predict an upsizing trend of greater ages as one proceeds to masses lower than 10^10 M_Sun. We find that the fraction of galaxies with very young stellar populations (more than half the stellar mass formed within the last 1.5 Gyr) is a function of present-day stellar mass, which peaks at 0.5% at m_crit=10^7.5-9.5 M_Sun, roughly corresponding to the masses of blue compact dwarfs. We predict that the stellar mass function of galaxies should not show a maximum at m_stars > 10^{5.5}, M_Sun, with a power-law stellar mass function with slope approx -1.6 if the IGM temperature in the outskirts of halos before reionization is set by H2 cooling. We speculate on the nature of the lowest mass galaxies.
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