  We study the infall of a subhalo in its parent halo due to dynamical
friction. Using expected mass and spatial distributions of subhaloes, in unison
with the derived infall time-scale, we calculate the expected merger stellar
mass growth rate (SMGR) of the central galaxy in two different models
(instantaneous and continuous merging). We find that our continuous merging
SMGR (which corresponds to smooth accretion from satellites) agrees with the
results of the Millennium-II simulation, predicting low growth rates for low
stellar masses ($10^{8}$ M$_{\odot}-10^{10}$ M$_{\odot}$) and accelerating
growth for high masses ($10^{10}$ M$_{\odot}-10^{12}$ M$_{\odot}$). Using the
derived formulas we study the relative contributions of minor and major mergers
to the total merger SMGR at various redshifts. Minor mergers contribute
$80\%-90\%$ in the low mass range for $z<4$, with major mergers becoming the
dominant merger type (80$\%-95\%$) at relatively high masses ($4\times 10^{10}$
M$_{\odot}$) for $z>1$. This suggests that most merger mass growth is due to
minor mergers. We derive an SMGR formula for the very early universe ($z>4$)
and use this to show that hierarchial merging of protogalaxies can lead to the
modern population of galaxies. Our overall analysis suggests that dynamical
friction is the primary cause of galaxy mergers.
