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Starting from the ∼50 000 quasars of the Sloan Digital Sky Survey for which Mg  ii  line width and 3000 Å monochromatic flux are available, we aim to study the dependence of the mass of active black holes on redshift. We focus on the observed distribution in the full width at half‐maximum–nuclear luminosity plane, which can be reproduced at all redshifts assuming a limiting  M  BH , a maximum Eddington ratio and a minimum luminosity (due to the survey flux limit). We study the  z ‐dependence of the best‐fitting parameters of assumed distributions at increasing redshift and find that the maximum mass of the quasar population evolves as  log ( M  BH(max) /M ⊙ ) ∼ 0.3 z + 9 , while the maximum Eddington ratio (∼0.45) is practically independent of cosmic time. These results are unaffected by the Malmquist bias.

Downsizing of supermassive black holes from the SDSS quasar survey