  This paper presents direct evidence for hierarchical galaxy assembly out to
redshifts z ~ 3. We identify major mergers using the model-independent CAS
(concentration, asymmetry, clumpiness) physical morphological system on
galaxies detected, and photometrically selected, in the WFPC2 and NICMOS Hubble
Deep Field North. We specifically use the asymmetric distributions of
rest-frame optical light measured through the asymmetry parameter (A) to
determine the fraction of galaxies undergoing major mergers as a function of
redshift (z), stellar mass (M_{*}), and absolute magnitude (M_{B}). We find
that the fraction of galaxies consistent with undergoing a major merger
increases with redshift for all galaxies, but most significantly, at 5 - 10
sigma confidence, for the most luminous and massive systems. The highest merger
fractions we find are 40% - 50% for galaxies with M_{B} < -21, or M_{*} > 10^10
M_0 at z > 2.5, i.e., objects identified as Lyman-break galaxies. We model the
merger fraction evolution in the form: f x (1+z)^m, finding m values ~4-6 for
the most luminous and massive galaxies. We use these merger fractions combined
with merger time scales calculated from N-body simulations to derive galaxy
merger rates to z ~ 3. We also use stellar masses of HDF-N galaxies to
determine the mass accretion rate of field galaxies involved in major mergers,
and how this changes with redshift. We further find that the fraction of
stellar mass density in galaxies involved in major mergers increases with
redshift. By comparing merger fractions predicted in Cold Dark Matter
semi-analytic models with our results there is a reasonably good agreement for
the largest and brightest systems, although there are more low-mass galaxy
mergers at lower redshifts than what these models predict. (abridged)
