  Using the BH masses deduced from the empirical relation of Kaspi et al.
(2000) and 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 in the gravitationally unstable region of the disc. 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. The accretion rate stays
always of the order of a few M$_{\odot}$/yr, indicating that the growing of the
BH is mass supply limited . Since the masses of the BH increases by one order
of magnitude in a few 10$^7$ years, it could explain why NLS1s appear to not
follow the same BH - bulge relation as other galaxies. NLS1s should thus play
an important role in shaping the mass function of local BHs. We discuss the
possibility that the masses could be systematically underestimated due to an
inclination effect, and we conclude that the accretion rates could thus be
strongly overestimated, but only in a small proportion of objects.
