The quest for the origin of the Jupiter family of comets includes inve
stigating the possibility that a large fraction of this population ori
ginates from past splitting events. In particular, one suggested scena
rio, albeit less attractive on physical grounds, maintains that a gian
t comet breakup is a major source of short-period comets. By simulatin
g such events and integrating the motions of the fictitious fragments
in an accurate solar system model for the typical lifetime of Jupiter
family comets, it is possible to check whether the outcome may or may
not be compatible with the observed orbital distribution. In this pape
r we present such integrations for a few typical progenitor orbits and
analyze the ensuing thermalization process with particular attention
to the Tisserand parameters. It is found that the sets of fragments lo
se their memory of a common origin very rapidly so that, in general te
rms, it is difficult to use the random appearance of the observed orbi
tal distribution as evidence against the giant comet splitting hypothe
sis.