We use the BH masses deduced from the empirical relation of Kaspi et al. (2000) between the size of the Broad Line Region (BLR) of Active Galactic Nuclei (AGN) and the optical luminosity, to compute their accretion rates in four samples of AGN, assuming that the optical luminosity is provided by the accretion disc. We show that Narrow Line Seyfert Galaxies 1 (NLS1s) accrete at super-Eddington rates, while their luminosity stays of the order of the Eddington limit. We take into account the possibility of a non-viscous energy release inversely proportional to the square of the distance in the gravitationally unstable region of the disc emitting a fraction of the optical luminosity. It leads to a smaller accretion rate and to a redder continuum than a standard disc, which agrees better with the observations. The observed bolometric luminosities appear to saturate at a few times the Eddington luminosity for super-Eddington accretion rates, as predicted by slim disc models. They favor a Kerr BH rather than a Schwarzschild one. Even when the accretion rate is super-Eddington, it stays always of the order of a few M_&sun;/yr, irrespective of the BH mass, indicating that the growing of the BH is mass-supply-limited and therefore regulated by an exterior mechanism, and not Eddington-limited. The mass of the BH increases by one order of magnitude in a few 10⁷ years, a time smaller than that necessary for changing the bulge mass. This is in agreement with recent claims that the BHs of NLS1s do not follow the same black hole - bulge relation as other galaxies. Since they represent about 10% of AGN up to a redshift of 0.5, these ``super-active'' phases should play an important role in shaping the mass function of local BHs. We finally discuss the possibility that the masses could be systematically underestimated due to an inclination effect, and we conclude that this could indeed be the case, and that the accretion rates could thus be strongly overestimated in a small fraction of objects, possibly explaining the existence of apparently extremely high accretors.