  We re-examine a two-dimensional forest-fire model via Monte-Carlo simulations
and show the existence of two length scales with different critical exponents
associated with clusters and with the usual two-point correlation function of
trees. We check resp. improve previously obtained values for other critical
exponents and perform a first investigation of the critical behaviour of the
slowest relaxational mode. We also investigate the possibility of describing
the critical point in terms of a distribution of the global density. We find
that some qualitative features such as a temporal oscillation and a power law
of the cluster-size distribution can nicely be obtained from such a model that
discards the spatial structure.
