  We use galaxy and dark halo data from the public database for the Millennium
Simulation to study the growth of galaxies in the De Lucia et al. (2006) model
for galaxy formation. Previous work has shown this model to reproduce many
aspects of the systematic properties and the clustering of real galaxies, both
in the nearby universe and at high redshift. It assumes the stellar masses of
galaxies to increase through three processes, major mergers, the accretion of
smaller satellite systems, and star formation. We show the relative importance
of these three modes to be a strong function of stellar mass and of redshift.
Galaxy growth through major mergers depends strongly on stellar mass, but only
weakly on redshift. Except for massive systems, minor mergers contribute more
to galaxy growth than major mergers at all redshifts and at all stellar masses.
For galaxies significantly less massive than the Milky Way, star formation
dominates the growth at all epochs. For galaxies significantly more massive
than the Milky Way, growth through mergers is the dominant process at all
epochs. At a stellar mass of $6\times 10^{10}M_\odot$, star formation dominates
at $z>1$ and mergers at later times. At every stellar mass, the growth rates
through star formation increase rapidly with increasing redshift. Specific star
formation rates are a decreasing function of stellar mass not only at $z=0$ but
also at all higher redshifts. For comparison, we carry out a similar analysis
of the growth of dark matter halos. In contrast to the galaxies, growth rates
depend strongly on redshift, but only weakly on mass. They agree qualitatively
with analytic predictions for halo growth.
