  We use N-body simulations and observationally-normalized relations between
dark matter halo mass, stellar mass, and cold gas mass to derive robust,
arguably inevitable expectations about the baryonic content of major mergers
out to redshift z~2. First, we find that the majority of major mergers (m/M >
0.3) experienced by Milky Way size dark matter halos should have been gas-rich,
and that gas-rich mergers are increasingly common at high redshift. Though the
frequency of major mergers into galaxy halos in our simulations greatly exceeds
the observed late-type galaxy fraction, the frequency of gas-poor major mergers
is consistent with the observed fraction of spheroid-dominated galaxies across
the halo mass range M_DM ~ 10^11-10^13 Msun. These results lend support to the
conjecture that mergers with high baryonic gas fractions play an important role
in building and/or preserving disk galaxies in the universe. Also, we find that
the overall fraction of a galaxy's cold baryons deposited directly via major
mergers is substantial. Approximately ~30% of the cold baryonic material in
M_star ~ 10^10 Msun$ (M_DM ~ 10^11.5 Msun) galaxies is accreted as cold gas in
major mergers. For more massive galaxies with M_star ~ 10^11 Msun (M_DM ~ 10^13
Msun) the fraction of baryons amassed in mergers is even higher, ~50%, but most
of these accreted baryons are delivered directly in the form of stars. This
baryonic mass deposition is almost unavoidable, and provides a limit on the
fraction of a galaxy's cold baryons that can originate in cold flows or from
hot halo cooling. (Abridged)
