  Large-scale simulations of the Centaur population are carried out. The
evolution of 23328 particles based on the orbits of 32 well-known Centaurs is
followed for up to 3 Myr in the forward and backward direction under the
influence of the 4 massive planets. The objects exhibit a rich variety of
dynamical behaviour with half-lives ranging from 540 kyr (1996 AR20) to 32 Myr
(2000 FZ53). The mean half-life of the entire sample of Centaurs is 2.7 Myr.
The data are analyzed using a classification scheme based on the controlling
planets at perihelion and aphelion, previously given in Horner et al (2003).
Transfer probabilities are computed and show the main dynamical pathways of the
Centaur population. The total number of Centaurs with diameters larger than 1
km is estimated as roughly 44300, assuming an inward flux of one new
short-period comet every 200 yrs. The flux into the Centaur region from the
Edgeworth-Kuiper belt is estimated to be 1 new object every 125 yrs. Finally,
the flux from the Centaur region to Earth-crossing orbits is 1 new
Earth-crosser every 880 yrs
