  In a previous paper, Collin & Hur\'e (2001), using a sample of Active
Galactic Nuclei (AGN) where the mass has been determined by reverberation
studies (Kaspi et al. 2000), have shown that if the optical luminosity is
emitted by a steady accretion disc, about half of the objects are accreting
close to or higher than the Eddington rate. We conclude here that this result
is unavoidable, unless the masses are strongly underestimated by reverberation
studies, which does not seem to be the case. There are three issues to the
problem: 1. Accretion proceeds at Eddington or super-Eddington rates through
thick discs. Several consequences follow: an anti-correlation between the line
widths of the lines and the Eddington ratios, and a decrease of the Eddington
ratio with an increasing black hole mass. Extrapolated to all quasars, these
results imply that the amount of mass locked in massive black holes should be
larger than presently thought. 2. The optical luminosity is not produced
directly by the gravitational release of energy, and super-Eddington rates are
not required. The optical luminosity has to be emitted by a dense and thick
medium located at large distances from the center (10$^3$ to $10^4$
gravitational radii). It can be due to reprocessing of the X-ray photons from
the central source in a geometrically thin warped disc, or in dense "blobs"
forming a geometrically thick system, which can be a part of the accretion flow
or the basis of an outflow. 3. Accretion discs are completely "non standard".
Presently neither the predictions of models nor the observed spectral
distributions are sufficient to help choosing between these solutions.
