  Quasars accreting matter at very high rates (known as extreme Population A
[xA] or super-Eddington accreting massive black holes) provide a new class of
distance indicators covering cosmic epochs from the present-day Universe up to
less than 1 Gyr from the Big Bang. The very high accretion rate makes it
possible that massive black holes hosted in xA quasars radiate at a stable,
extreme luminosity-to-mass ratio. This in turns translates into stable physical
and dynamical conditions of the mildly ionized gas in the quasar low-ionization
line emitting region. In this contribution, we analyze the main optical and UV
spectral properties of extreme Population A quasars that make them easily
identifiable in large spectroscopic surveys at low-z (z < 1) and intermediate-z
(2 < z < 2.6), and the physical conditions that are derived for the formation
of their emission lines. Ultimately, the analysis supports the possibility of
identifying a virial broadening estimator from low-ionization line widths, and
the conceptual validity of the redshift-independent luminosity estimates based
on virial broadening for a known luminosity-to-mass ratio.
