  We present results from our Very Large Telescope large program to study the
dynamical evolution of local Ultraluminous Infrared Galaxies (ULIRGs) and QSOs.
This paper is the second in a series presenting the stellar kinematics of 54
ULIRGs, derived from high resolution, long-slit H- and K-band spectroscopy. The
data presented here, including observations of 17 new targets, are mainly
focused on sources that have coalesced into a single nucleus. The stellar
kinematics, extracted from the CO ro-vibrational bandheads in our spectra,
indicate that ULIRG remnants are dynamically heated systems with a mean
dispersion of 161 km/s. The combination of kinematic, structural, and
photometric properties of the remnants indicate that they mostly originate from
major mergers and that they result in the formation of systems supported by
random motions, therefore, elliptical galaxies. The peak of the velocity
dispersion distribution and the locus of ULIRGs on the fundamental plane of
early-type galaxies indicate that the end products of ultraluminous mergers are
typically moderate-mass ellipticals (of stellar mass ~10^10 - 10^11 M_sun).
Converting the host dispersion into black hole mass with the aid of the
M_BH-sigma relation yields black hole mass estimates of the order 10^7 - 10^8
M_sun and high accretion rates with Eddington efficiencies often >0.5.
