We present detailed clustering measurements for a flux-limited sample of ∼14 000 quasars extracted from the 2dF QSO Redshift Survey 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/h −1 Mpc 20. Fitting the data with a biased cold dark matter model and using a frequentist analysis (the F-test), we

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... 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 data set 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 .