Recently, the first collisional family was identified in the trans-Neptunian belt (otherwise known as the Edgeworth–Kuiper belt), providing direct evidence of the importance of collisions between trans-Neptunian objects (TNOs). The family consists of the dwarf planet (136108) Haumea (formerly 2003 EL61), located at a semimajor axis, a, of ∼43 au, and at least 10 other ∼100-km-sized TNOs located in the region a= 42–44.5 au. In this work, we model the long-term orbital evolution (4 Gyr) of an ensemble of fragments (particles) representing hypothetical post-collision distributions at the time of the family’s birth based on our limited current understanding of the family’s creation and of asteroidal collision physics. We consider three distinct scenarios, in which the kinetic energy of dispersed particles was varied such that their mean ejection velocities (veje) were of the order of 200, 300 and 400 m s−1, respectively. Each simulation considered resulted in collisional families that reproduced that currently observed, despite the variation in the initial conditions modelled. The results suggest that 60–75 per cent 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 Δa∼ 6–12 au, Δe∼ 0.1–0.15 and Δi∼ 7°–10°, with the exact range covered being proportional to veje used in the model. Most of the survivors populated the so-called classical and detached regions of the trans-Neptunian belt, whilst a minor fraction either entered the scattered disc reservoir (<1 per cent) or were captured in Neptunian mean-motion resonances (<10 per cent). In addition, except for those fragments located near strong resonances (such as the 5:3 and 7:4), 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, although future work is needed to confirm this result.