Black hole masses in Active Galactic Nuclei have been determined in 35 objects through reverberation mapping of the emission line region. I mention some uncertainties of the method, such as the “scale factor” relating the Virial Product to the mass, which depends on the unknown structure and dynamics of the Broad Line Region.
When the black hole masses are estimated indirectly using the empirical size-luminosity relation deduced from this method, the uncertainties can be larger, especially when the relation is extrapolated to high and low masses and/or luminosities. In particular they lead to Eddington ratiosof the order of unity in samples of Narrow Line Seyfert 1. As the optical-UV luminosity is provided by the accretion disk, the accretion rates can be determined and are found to be much larger than the Eddington rates.
So, accretion must be performed at a super-critical rate through a slim disk, resulting in rapid growth of the black holes. The alternative is that the mass determination is wrong at this limit.
