  Exoplanetary systems host giant planets on substantially non-circular,
close-in orbits. We propose that these eccentricities arise in a phase of giant
impacts, analogous to the final stage of Solar System assembly that formed
Earth's Moon. In this scenario, the planets scatter each other and collide,
with corresponding mass growth as they merge. We numerically integrate an
ensemble of systems with varying total planet mass, allowing for collisional
growth, to show that (1) the high-eccentricity giants observed today may have
formed preferentially in systems of higher initial total planet mass, and (2)
the upper bound on the observed giant planet eccentricity distribution is
consistent with planet-planet scattering. We predict that mergers will produce
a population of high-mass giant planets between 1 and 8 au from their stars.
