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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- (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, P.M. wishes to thank the Scientific Organizing Committee of the Symposium on the Physics of Ionized Gases (SPIG 2018) meeting for inviting the topical lecture on which this paper is based, and acknowledges the Programa de Estancias de Investigación (PREI) No. DGAP/DFA/2192/2018 of Universidad Nacional Autónoma de México (UNAM), where this paper was written. The relevant research is part of the project 176001 “Astrophysical spectroscopy of extragalactic objects” and 176003 “Gravitation and the large scale structure of the Universe” supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia. M.L.M.-A. acknowledges a CONACyT postdoctoral fellowship. A.d.O. and M.L.M.-A. acknowledge financial support from the Spanish Ministry for Economy and Competitiveness through Grant Nos. AYA2013-42227-P and AYA2016-76682-C3-1-P. M.L.M.-A, P.M. and M.D. acknowledge funding from the INAF PRIN-SKA 2017 program 1.05.01.88.04. D.D. and A.N. acknowledge support from CONACyT through Grant No. CB221398. D.D. and C.A.N. are also thankful for the support from Grant No. IN108716 53 PAPIIT, UNAM, We acknowledge support by the CSIC Open Access Publication Initiative through its Unit of Information Resources for Research (URICI)