We compare all the available observational data on the redshift evolution of the total stellar mass and star formation rate density in the Universe with the mass and accretion rate density evolution of supermassive black holes , estimated from the hard X-ray selected luminosity function of quasars and active galactic nuclei ( AGN ) .
We find that on average black hole mass must have been higher at higher redshift for given spheroid stellar mass .
Moreover , we find negative redshift evolution of the disk/irregulars to spheroid mass ratio .
The total accretion efficiency is constrained to be between 0.06 and 0.12 , depending on the exact value of the local SMBH mass density , and on the critical accretion rate below which radiatively inefficient accretion may take place .