Low- and high-z highly accreting quasars in the 4D Eigenvector 1 context

Highly accreting quasars are characterized by distinguishing properties in the 4D eigenvector 1 parameter space that make them easily recognizable over a broad range range of redshift and luminosity. The 4D eigenvector 1 approach allows us to define selection criteria that go beyond the restriction to Narrow Line Seyfert 1s identified at low redshift. These criteria are probably able to isolate sources with a defined physical structure i.e., a geometrically thick, optically thick advection-dominated accretion disk (a slim disk). We stress that the importance of highly accreting quasars goes beyond the understanding of the details of their physics: their Eddington ratio is expected to saturate toward values of order unity, making them possible cosmological probes.