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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 can radiate at a stable, extreme luminosity-to-mass ratio. This in turn 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- (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>z</mi> <mo>≲</mo> <mn>1</mn> </mrow> </semantics> </math> </inline-formula>) and intermediate-<i>z</i> (2 <inline-formula> <math display="inline"> <semantics> <mrow> <mo>≲</mo> <mi>z</mi> <mo>≲</mo> </mrow> </semantics> </math> </inline-formula> 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.