  This paper describes the simulation of realistic Monte-Carlo extragalactic
catalogues, aimed at comparing the behaviour of cosmological tests versus input
parameters. QSO catalogues are built on a Luminosity Function derived from data
through suitable computation of individual maximum volumes in complete (but
magnitude- and redshift-limited) samples requiring neither of redshift nor of
apparent magnitude histogram. The values of the evolution parameter are derived
for various cosmologies, corresponding to <V/Vmax>=1/2 in the sample of 400
Ultra-Violet Excess (UVX) QSOs (Boyle et al 1990). The various luminosity
functions are compared, both for the whole sample and in redshift bins. An
evolution characteristic time is defined and computed, depending strongly on
the cosmology, but practically constant when expressed in terms of the age of
the Universe. Algorithms are given for producing unbiased or biased catalogues
based on the null hypothesis that the objects are uniformly distributed in
volume but suffer Pure Luminosity Evolution.
