  We present the results of a series of empirical computations regarding the
role of major mergers in forming the stellar masses of modern galaxies based on
measurements of galaxy merger and star formation histories from z~0.5-3. We
re-construct the merger history of normal field galaxies from z~3 to z~0 as a
function of initial mass using published pair fractions and merger fractions
from structural analyses. We calibrate the observed merger time-scale and mass
ratios for galaxy mergers using self-consistent N-body models of mergers,
composed of dark matter and stars, with mass ratios from 1:1 to 1:5 with
various orbital properties and viewing angles. We use these simulations to
determine the time-scales and mass ratios that produce structures that would be
identified as major mergers. Based on these calculations we argue that a
typical massive galaxy at z~3 with M_{*} > 10^{10} M_0 undergoes
4.4^{+1.6}_{-0.9} major mergers at z > 1. We find that by z~1.5 the stellar
mass of an average massive galaxy is relatively established, a scenario
qualitatively favored in a lambda dominated universe. We argue that the final
masses of these systems increases by as much as a factor of 100 allowing
Lyman-break galaxies, which tend to have low stellar masses, to become the most
massive galaxies in today's universe with M > M^{*}. Induced star formation
however only accounts for 10-30% of the stellar mass formed in these galaxies
at z < 3. A comparison to semi-analytic models of galaxy formation shows that
Cold Dark Matter (CDM) models consistently under-predict the merger fraction,
and rate of merging, of massive galaxies at high redshift. This suggests that
massive galaxy formation occurs through more merging than predicted in CDM
models, rather than a rapid early collapse.
