  We have used composite spectra generated from more than 22000 QSOs observed
in the course of the 2dF and 6dF QSO Redshift Surveys to investigate the
relationship between the velocity width of emission lines and QSO luminosity.
We find that the velocity width of the broad emission lines Hbeta, Hgamma,
MgII, CIII] and CIV are correlated with the continuum luminosity, with a
significance of more than 99 per cent. Of the major narrow emission lines
([OIII] 5007, [OII] 3727, NeIII 3870 and NeV 3426) only [OIII] exhibits a
significant correlation between line width and luminosity. Assuming that the
gas is moving in Keplerian orbits and that the radius of the broad line region
is related to the QSO continuum luminosity, we use the velocity widths of the
broad lines to derive average black hole masses for the QSOs contributing to
the composite spectra. The resultant QSO mass-luminosity relationship is
consistent with M ~ L^0.97+-0.16. We find that the correlation between line
width and redshift, if present, must be weak, and only CIV shows significant
evidence of evolution. This enables us to constrain the redshift evolution of
the black hole mass-luminosity ratio to be ~(1+z)^beta with beta ~< 1, much
less than the ~(1+z)^3 evolution seen in QSO luminosity evolution. Assuming
that the motion of the broad line region gas is Keplerian and that its radius
depends on the QSO luminosity, our models indicate that the observed weak
redshift dependence is too small for the observed QSO luminosity function to be
due to the evolution of a single long-lived population of sources.
