  We investigate the bright cut-off of the [OIII]l5007 planetary nebula
luminosity function (PNLF), that has been suggested as a powerful extragalactic
distance indicator. Theoretical PNLFs are constructed via Monte-Carlo
simulations of populations of PNe, whose individual properties are described
with the aid of recent PN synthetic models (Marigo et al. 2001), coupled to a
detailed photoionisation code (CLOUDY). The basic dependences of the cut-off
magnitude M* are then discussed. We find that: (i) In galaxies with recent or
ongoing star formation, the modelled PNLF present M* values between -4 and -5,
very close to the observationally-calibrated value for the LMC. (ii) In these
galaxies, the PNLF cut-off is produced by PNe with progenitor masses of about
2.5 Msun, while less massive stars give origin to fainter PNe. As a consequence
M* is expected to depend strongly on the age of the last burst of star
formation, dimming by as much as 5 mag as we go from young to 10-Gyr old
populations. (iii) Rather than on the initial metallicity of a stellar
population, M* depends on the actual [O/H] of the observed PNe, a quantity that
may differ significantly from the initial value (due to dredge-up episodes),
especially in young and intermediate-age PN populations. (iv) Also the
transition time from the end of AGB to the PN phase, and the nuclear-burning
properties (i.e. H- or He-burning) of the central stars introduce
non-negligible effects on M*. The strongest indication derived from the present
calculations is a serious difficulty to explain the age-invariance of the
cut-off brightness over an extended interval, say from 1 to 13 Gyr, that
observations of PNLFs in galaxies of late-to-early type seem to suggest.
