This paper presents direct evidence for hierarchical galaxy assembly out to redshifts z \sim 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 _ { \star } ) , 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 _ { \star } > 10 ^ { 10 } M _ { \odot } at z > 2.5 , i.e. , objects identified as Lyman-break galaxies .
Using these results , we model the merger fraction evolution in the form : f _ { m } ( A , M _ { \star } , M _ { B } , z ) = f _ { 0 } ~ { } \times ( 1 + z ) ^ { m _ { A } } .
We find m _ { A } values \sim 4 - 6 for the most luminous and massive galaxies , while lower mass and less luminous galaxies have smaller m _ { A } values .
We use these merger fractions , combined with merger time scales calculated from N-body simulations , to derive galaxy merger rates to z \sim 3 .
We also use stellar masses of HDF-N galaxies to determine the mass accretion rate of field galaxies involved in major mergers .
We find an average stellar mass accretion rate of \dot { M } _ { G } \sim 4 \times 10 ^ { 8 } 
M _ { \odot } Gyr ^ { -1 } galaxy ^ { -1 } at z \sim 1 for galaxies with stellar masses M _ { \star } > 10 ^ { 9 } M _ { \odot } .
This accretion rate changes with redshift as : \dot { M } _ { G } = 1.6 \times 10 ^ { 8 } ( 1 + z ) ^ { 0.99 \pm 0.32 } 
M _ { \odot } Gyr ^ { -1 } galaxy ^ { -1 } .
We also find that the fraction of stellar mass density in galaxies involved in major mergers increases with redshift , with a peak mass fraction \sim 0.5 for the brightest , M _ { B } < -21 , and most massive , M _ { \star } > 10 ^ { 10 } M _ { \odot } , systems near z \sim 2.5 .
By comparing merger fractions predicted in Cold Dark Matter semi-analytic models with our results we find a reasonably good agreement for the largest and brightest systems , although we find more low-mass galaxy mergers at lower redshifts than what these models predict .