  We apply a simple, one-equation, galaxy formation model on top of the halos
and subhalos of a high-resolution dark matter cosmological simulation to study
how dwarf galaxies acquire their mass and, for better mass resolution, on over
10^5 halo merger trees, to predict when they form their stars. With the first
approach, we show that the large majority of galaxies within group- and
cluster-mass halos have acquired the bulk of their stellar mass through gas
accretion and not via galaxy mergers. We deduce that most dwarf ellipticals are
not built up by galaxy mergers. With the second approach, we constrain the star
formation histories of dwarfs by requiring that star formation must occur
within halos of a minimum circular velocity set by the evolution of the
temperature of the IGM, starting before the epoch of reionization. We
qualitatively reproduce the downsizing trend of greater ages at greater masses
and predict an upsizing trend of greater ages as one proceeds to masses lower
than m_crit. We find that the fraction of galaxies with very young stellar
populations (more than half the mass formed within the last 1.5 Gyr) is a
function of present-day mass in stars and cold gas, which peaks at 0.5% at
m_crit=10^6-8 M_Sun, corresponding to blue compact dwarfs such as I Zw 18. We
predict that the baryonic mass function of galaxies should not show a maximum
at masses above 10^5.5, M_Sun, and we speculate on the nature of the lowest
mass galaxies.
