We explore the evolution of the specific star formation rate (SSFR) for 3.6um-selected galaxies of different M_* in the COSMOS field. The average SFR for sub-sets of these galaxies is estimated with stacked 1.4GHz radio continuum emission. We separately consider the total sample and a subset of galaxies (SF) that shows evidence for substantive recent star formation in the rest-frame optical SED. At 0.21.5 there is tentative evidence for an upper SSFR-limit that an average galaxy cannot exceed. It is suggested by a flattening of the SSFR-M_* relation (also for SF sources), but affects massive (>10^10M_Sun) galaxies only at the highest z. Below z=1.5 there thus is no direct evidence that galaxies of higher M_* experience a more rapid waning of their SSFR than lower M_* SF systems. In this sense, the data rule out any strong 'downsizing'. We combine our results with recent measurements of the galaxy (stellar) mass function in order to determine the characteristic mass of a SF galaxy (M_*=10^(10.6\pm0.4)M_Sun). In this sense, too, there is no 'downsizing'. Our analysis constitutes the most extensive SFR density determination with a single technique to z=3. Recent Herschel results are consistent with our results, but rely on far smaller samples.