  We investigate the role that dry mergers play in the build-up of massive
galaxies within the cold dark matter paradigm. Implementing an empirical
shut-off mass scale for star formation, we find a nearly constant dry merger
rate of $ \sim 6 \times 10^{-5}$ Mpc$^{-3}$ Gyr$^{-1}$ at $z \leq 1$ and a
steep decline at larger z. Less than half of these mergers are between two
galaxies that are morphologically classified as early-types, and the other half
is mostly between an early-type and late-type galaxy. Latter are prime
candidates for the origin of tidal features around red elliptical galaxies. The
introduction of a transition mass scale for star formation has a strong impact
on the evolution of galaxies, allowing them to grow above a characteristic mass
scale of $M_{*,c} \sim 6.3 \times 10^{10}$ M$_{\odot}$ by mergers only. As a
consequence of this transition, we find that around $M_{*,c}$, the fraction of
1:1 mergers is enhanced with respect to unequal mass major mergers. This
suggest that it is possible to detect the existence of a transition mass scale
by measuring the relative contribution of equal mass mergers to unequal mass
mergers as a function of galaxy mass. The evolution of the high-mass end of the
luminosity function is mainly driven by dry mergers at low z. We however find
that only $10% -20%$ of galaxies more massive than $M_{*,c}$ experience dry
major mergers within their last Gyr at any given redshift $z \le 1$.
