We present the 1 kpc resolution 12CO imaging study of 37 optically selected local merger remnants using new and archival interferometric maps obtained with ALMA, CARMA, the Submillimeter Array, and the Plateau de Bure Interferometer. We supplement a sub-sample with single-dish measurements obtained at the Nobeyama Radio Observatory 45 m telescope for estimating the molecular gas mass (107 – 11 M ☉) and evaluating the missing flux of the interferometric measurements. Among the sources with robust CO detections, we find that 80% (24/30) of the sample show kinematical signatures of rotating molecular gas disks (including nuclear rings) in their velocity fields, and the sizes of these disks vary significantly from 1.1 kpc to 9.3 kpc. The size of the molecular gas disks in 54% of the sources is more compact than the K-band effective radius. These small gas disks may have formed from a past gas inflow that was triggered by a dynamical instability during a potential merging event. On the other hand, the rest (46%) of the sources have gas disks that are extended relative to the stellar component, possibly forming a late-type galaxy with a central stellar bulge. Our new compilation of observational data suggests that nuclear and extended molecular gas disks are common in the final stages of mergers. This finding is consistent with recent major-merger simulations of gas-rich progenitor disks. Finally, we suggest that some of the rotation-supported turbulent disks observed at high redshifts may result from galaxies that have experienced a recent major merger
