  Quasars accreting matter at very high rates (known as extreme Population A
[xA]) may provide a new class of distance indicators covering cosmic epochs
from present day up to less than 1 Gyr from the Big Bang. We report on the
developments of a method that is based on "virial luminosity" estimates from
measurements of emission line widths of xA quasars. The approach is
conceptually equivalent to the virial estimates based on early and late type
galaxies. The main issues related to the cosmological application of luminosity
estimates from xA quasar line widths are the identification of proper emission
lines whose broadening is predominantly virial over a wide range of luminosity,
and the assessment of the effect of the emitting region orientation with
respect to the line of sight. We report on recent developments concerning the
use of the AlIII 1860 intermediate ionisation line and of the Hydrogen Balmer
line H$\beta$ as "virial broadening estimators."
