In a previous paper we showed that the radio sources selected by combining large areas radio and optical surveys, present a strong deficit of radio emission with respect to 3CR radio-galaxies matched in line emission luminosity. We argued that the prevalence of sources with luminous extended radio structures in high flux limited samples is due to a selection bias. Sources with low radio power form the bulk of the radio-loud AGN population but are still virtually unexplored. We here analyze their photometric and spectroscopic properties. From the point of view of their emission lines, the majority of the sample are Low Excitation Galaxies (LEG), similar to the 3CR objects at the same level of line luminosity. The hosts of LEG are red, massive Early-Type Galaxies (ETG) with large black holes masses , statistically indistinguishable from the hosts of low redshift 3CR/LEG sources. No genuine radio-loud LEG could be found associated with black holes with a mass substantially lower than 10^8 M(sun) or with a late type host. The fraction of galaxies with signs of star formation (5%) is similar to what is found in both the quiescent ETG and 3CR/LEG hosts. We conclude that the deficit in radio emission cannot be ascribed to differences in the properties of their hosts. We argue that instead this could be due to a temporal evolution of the radio luminosity. A minority (10%) of the sample show rather different properties, being associated with low black hole masses, with spiral galaxies, or showing a high excitation spectrum. In general these outliers are the result of the contamination from Seyfert and from galaxies where the radio emission is powered by star formation. For the objects with high excitation spectra there is no a clear discontinuity in either the host or nuclear properties as they span from radio-quiet and radio-loud AGN.
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