Massive quiescent galaxies at z>1 have been found to have small physical sizes, hence to be superdense. Several mechanisms, including minor mergers, have been proposed for increasing galaxy sizes from high- to low-z. We search for superdense massive galaxies in the WIde-field Nearby Galaxy-cluster Survey (WINGS) of X-ray selected galaxy clusters at 0.04<z<0.07. We discover a significant population of superdense massive galaxies with masses and sizes comparable to those observed at high redshift. They approximately represent 22% of all cluster galaxies more massive than 3x10^10Msol, are mostly S0 galaxies, have a median effective radius <Re> =1.61+/-0.29kpc, a median Sersic index <n> = 3.0+/-0.6, and very old stellar populations with a median mass-weighted age of 12.1+/-1.3Gyr. We calculate a number density of 2.9x10^-2Mpc^-3 for superdense galaxies in local clusters, and a hard lower limit of 1.3x10^-5Mpc^-3 in the whole comoving volume between z = 0.04 and z = 0.07. We find a relation between mass, effective radius and luminosity-weighted age in our cluster galaxies, which can mimic the claimed evolution of the radius with redshift, if not properly taken into account. We compare our data with spectroscopic high-z surveys and find that -when stellar masses are considered- there is consistency with the local WINGS galaxy sizes out to z~2, while a discrepancy of a factor of 3 exists with the only spectroscopic z>2 study. In contrast, there is strong evidence for a large evolution in radius for the most massive galaxies with M*>4x10^11Msol compared to similarly massive galaxies in WINGS, i.e. the BCGs.
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