  We present detailed clustering measurements for a flux limited sample of
14,000 quasars extracted from the 2dF QSO Redshift Survey (2QZ) in the redshift
range 0.8<z<2.1. After splitting the sample into three redshift bins and each
of them into six luminosity intervals, we estimate the quasar projected auto
and cross-correlation functions at a given redshift for separations 3 <
r/(Mpc/h) < 20. Fitting the data with a biased CDM model and using a
frequentist analysis (the F-test), we find that models with luminosity
dependent clustering are statistically favoured at the 95 per cent confidence
level for z>1.3. On the other hand, a number of tests based on information
theory and Bayesian statistics show only marginal evidence for luminosity
dependent clustering. Anyway, the quality of the data is not good enough to
accurately quantify how quasar biasing depends on luminosity. We critically
discuss the limitations of our dataset and show that a much larger sample is
needed to rule out current models for luminosity segregation. Studying the
evolution of the clustering amplitude with redshift, we detect an increase of
the quasar correlation length with lookback time at the 99.3 per cent
confidence level. Adopting the concordance cosmological model, we discuss the
evolution of quasar biasing with cosmic epoch and show that quasars are
typically hosted by dark matter haloes with mass ~10^{13} M_sol.
