Star clusters or asterisms? 2MASS CMD and structural analyses of 15 challenging targets

Context. Poorly-populated star clusters may have photometric and structural properties not much different from asterisms, to the point that, in some cases, widely-used databases present conflicting classifications. Aims. We investigate the nature of a sample of challenging targets that have been classified either as star clusters or asterisms in different studies. A few objects are studied for the first time. Methods. The analysis employs 2MASS photometry, field-star decontamination, to enhance the intrinsic colour-magnitude diagram (CMD) morphology, and colour-magnitude filters, for high contrast stellar radial density profiles (RDPs). Results. Based on properties derived from field-star decontaminated CMDs, and structural parameters from RDPs, we find that Pismis 12, IC1434, Juchert 10, Ruprecht 30, NGC3519, Herschel 1, Mayer 1, and Muzzio 1 are open clusters with ages within 5Myr-1.3Gyr. Ruprecht 129, 130, 140, and 146 are borderline cases, being rather poorly-populated, with evolutionary sequences and RDPs suggesting star clusters. Dolidze 39, BH79, and Ruprecht 103, have CMDs and RDPs typical of asterisms. Conclusions. When a low stellar population is associated with a dense field contamination and/or important differential reddening, only a thin line separates star clusters and asterisms. These cases require specific analytical tools to establish their nature.