  We demonstrate that the luminosity function of the recently detected
population of star-forming galaxies and the QSO luminosity function at z=3 can
be matched with the mass function of dark matter haloes predicted by
hierarchical cosmogonies for lifetimes of optically bright QSOs in the range
10^6 to 10^8 yr. We suggest that the mass of supermassive black holes may be
limited by the back-reaction of the emitted energy on the accretion flow in a
self-gravitating disc. This would imply a relation of black hole to halo mass
of the form M_bh ~(v_halo)^5 and a typical duration of the optically bright QSO
phase of a few times 10^7 yr. The high integrated mass density of black holes
inferred from recent black hole mass estimates in nearby galaxies may indicate
that the overall efficiency of supermassive black holes for producing blue
light is smaller than previously assumed. We discuss three possible accretion
modes with low optical emission efficiency: (i) accretion at far above the
Eddington rate, (ii) accretion obscured by dust, and (iii) accretion below the
critical rate leading to an advection dominated accretion flow lasting for a
Hubble time. We further argue that accretion with low optical efficiency might
be closely related to the origin of the hard X-ray background and that the
ionizing background might be progressively dominated by stars rather than QSOs
at higher redshift.
