Context. Despite progress in the theoretical knowledge of open cluster remnants and the growing search for observational identifications in recent years, open questions still remain. The methods used to analyze open cluster remnants and criteria to define them as physical systems are not homogeneous. In this work we present a systematic method for studying these objects that provides a view of their properties and allows their characterization. Aims. Eighteen remnant candidates are analyzed by

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... eans of photometric and proper motion data. These data provide information on objects and their fields. We establish criteria for characterizing open cluster remnants, taking observational uncertainties into account. Methods. 2MASS J and H photometry is employed (i) to study structural properties of the objects by means of radial stellar density profiles, (ii) to test for any similarity between objects and fields with a statistical comparison method applied to the distributions of stars in the CMDs, and (iii) to obtain ages, reddening values, and distances from the CMD, taking an index of isochrone fit into account. The UCAC2 proper motions allowed an objective comparison between objects and large solid angle offset fields. Results. The objective analysis based on the present methods indicates 13 open-cluster remnants in the sample. Evidence of the presence of binary stars is found, as expected for dynamically evolved systems. Finally, we infer possible evolutionary stages among remnants from the structure, proper motion, and CMD distributions. The low stellar statistics for individual objects is overcome by means of the construction of composite proper motion and CMD diagrams. The distributions of remnants in the composite diagrams resemble the single-star and unresolved binary star distributions of open clusters.