  We present a targeted follow-up Hubble Space Telescope WFC3 F160W imaging
study of very massive galaxies $(\log(M_{\rm{star}}/M_{\odot})> 11.2)$ selected
from a combination of ground-based near-infrared galaxy surveys (UltraVISTA,
NMBS-II, UKIDSS UDS) at $1.5<z<3$. We find that these galaxies are diverse in
their structures, with $\sim1/3$ of the targets being composed of close pairs,
and span a wide range in sizes. At $1.5<z<2.5$, the sizes of both star-forming
and quiescent galaxies are consistent with the extrapolation of the stellar
mass-size relations determined at lower stellar masses. At $2.5<z<3.0$,
however, we find evidence that quiescent galaxies are systematically larger
than expected based on the extrapolation of the relation derived using lower
stellar mass galaxies. We used the observed light profiles of the blended
systems to decompose their stellar masses and investigate the effect of the
close pairs on the measured number densities of very massive galaxies in the
early universe. We estimate correction factors to account for close-pair blends
and apply them to the observed stellar mass functions measured using
ground-based surveys. Given the large uncertainties associated with this
extreme population of galaxies, there is currently little tension between the
(blending-corrected) number density estimates and predictions from theoretical
models. Although we currently lack the statistics to robustly correct for
close-pair blends, we show that this is a systematic effect which can reduce
the observed number density of very massive galaxies by up to a factor of
$\sim1.5$, and should be accounted for in future studies of stellar mass
functions.
