We have explored prevailing modes of galaxy growth for redshifts z ~ 6-14, comparing substantially overdense and normal regions of the universe, using high-resolution zoom-in cosmological simulations. Such rare overdense regions have been projected to host high-z quasars. We demonstrate that galaxies in such environments grow predominantly by a smooth accretion from cosmological filaments which dominates the mass input from major, intermediate and minor mergers. We find that by z ~6, the accumulated galaxy mass fraction from mergers falls short by a factor of 10 of the cumulative accretion mass for galaxies in the overdense regions, and by a factor of 5 in the normal environments. Moreover, the rate of the stellar mass input from mergers also lies below that of an in-situ star formation (SF) rate. The fraction of stellar masses in galaxies contributed by mergers in overdense regions is ~12%, and ~33% in the normal regions, at these redshifts. Our median SF rates for ~few X 10^9 Mo galaxies agrees well with the recently estimated rates for z ~ 7 galaxies from Spitzers SURF-UP survey. Finally, we find that the main difference between the normal and overdense regions lies in the amplified growth of massive galaxies in massive dark matter halos. This leads to the formation of >= 10^{10} Mo galaxies due to the ~100-fold increase in mass during the above time period. Such galaxies are basically absent in the normal regions at these redshifts.
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