  The Oort Cloud, the Kuiper Belt and the Scattered Disk are dynamically
distinct populations of small bodies evolving in the outer regions of the Solar
System. Whereas their collisional activity is now quiet, gravitational
interactions with giant planets may have shaped these populations both
dynamically and collisionally during their formation. Using a hybrid approach
(Charnoz & Morbidelli 2003), the present paper tries to couple the primordial
collisional and dynamical evolution of these three populations in a
self-consistent way. A critical parameter is the primordial size-distribution.
We show that the initial planetesimal size distribution that allows an
effective mass depletion of the Kuiper belt by collisional grinding, would
decimate also the population of comet-size bodies that end in the Oort Cloud
and, in particular, in the Scattered Disk. As a consequence, the Scattered Disk
and the Oort Cloud would be too anemic, by a factor 20 to 100, relative to the
estimates achieved from the observation of the fluxes of long period and
Jupiter family comets, respectively. For these two reservoirs to have a
sufficient number of comets, the initial size distribution in the planetesimal
disk had to be such that the mass depletion by collisional erosion of in the
Kuiper belt was negligible. Consequently, the current mass deficit of the
Kuiper belt, needs to be explained by dynamical mechanisms.
