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 ^ { -1 } . 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 \sim 10 ^ { 10 } -10 ^ { 11 } M _ { \odot } ) . 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 _ { \odot } and high accretion rates with Eddington efficiencies often > 0.5 .