  Recently, the first collisional family was identified in the trans-Neptunian
belt. The family consists of Haumea and at least ten other ~100km-sized
trans-Neptunian objects (TNOs) located in the region a = 42 - 44.5 AU. In this
work, we model the long-term orbital evolution of an ensemble of fragments
representing hypothetical post-collision distributions at the time of the
family's birth. We consider three distinct scenarios, in which the kinetic
energy of dispersed particles were varied such that their mean ejection
velocities (veje) were of order 200 m/s, 300 m/s and 400 m/s, respectively.
Each simulation considered resulted in collisional families that reproduced
that currently observed. The results suggest that 60-75% of the fragments
created in the collision will remain in the trans-Neptunian belt, even after 4
Gyr of dynamical evolution. The surviving particles were typically concentrated
in wide regions of orbital element space centred on the initial impact
location, with their orbits spread across a region spanning {\Delta}a ~ 6-12
AU, {\Delta}e ~ 0.1-0.15 and {\Delta}i ~ 7-10{\deg}. Most of the survivors
populated the so-called Classical and Detached regions of the trans-Neptunian
belt, whilst a minor fraction entered the Scattered Disk reservoir (<1%), or
were captured in Neptunian mean motion resonances (<10%). In addition, except
for those fragments located near strong resonances, the great majority
displayed negligible long-term orbital variation. This implies that the orbital
distribution of the intrinsic Haumean family can be used to constrain the
orbital conditions and physical nature of the collision that created the
family, billions of years ago. Indeed, our results suggest that the formation
of the Haumean collisional family most likely occurred after the bulk of
Neptune's migration was complete, or even some time after the migration had
completely ceased.
