We present in this paper an analysis of the faint and red near-infrared selected galaxy population found in near-infrared imaging from the Palomar Observatory Wide-Field Infrared Survey. This survey covers 1.53 deg^2 to 5-sigma detection limits of K_vega = 20.5-21 and J_vega = 22.5, and overlaps with the DEEP2 spectroscopic redshift survey. We discuss the details of this NIR survey, including our J and K band counts. We show that the K-band galaxy population has a redshift distribution that varies with K-magnitude, with most K < 17 galaxies at z < 1.5 and a significant fraction (38.3+/-0.3%) of K > 19 systems at z > 1.5. We further investigate the stellar masses and morphological properties of K-selected galaxies, particularly extremely red objects, as defined by (R-K) > 5.3 and (I-K) > 4. One of our conclusions is that the ERO selection is a good method for picking out galaxies at z > 1.2, and within our magnitude limits, the most massive galaxies at these redshifts. The ERO limit finds 75% of all M_* > 10^{11} M_0 galaxies at z ~ 1.5 down to K_vega = 19.7. We further find that the morphological break-down of K < 19.7 EROs is dominated by early-types (57+/-3%) and peculiars (34+/-3%). However, about a fourth of the early-types are distorted ellipticals, and within CAS parameter space these bridge the early-type and peculiar population, suggesting a morphological evolutionary sequence. We also investigate the use of a (I-K) > 4 selection to locate EROs, finding that it selects galaxies at slightly higher average redshifts (<z> = 1.43+/-0.32) than the (R-K) > 5.3 limit with <z> = 1.28+/-0.23. Finally, by using the redshift distribution of K < 20 selected galaxies, and the properties of our EROs, we are able to rule out all monolithic collapse models for the formation of massive galaxies.
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