© 2016 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.We present the Dark-ages Reionization and Galaxy formation Observables from Numerical Simulations (DRAGONS) programme and Tiamat, the collisionless N-body simulation programme upon which DRAGONS is built. The primary trait distinguishing Tiamat from other large simulation programme is its density of outputs at high redshift (100 from z = 35 to z = 5; roughly one every 10 Myr) enabling the construction of very accurate merger trees at an epoch when galaxy formation is rapid and mergers extremely frequent. We find that the friends-of-friends halo mass function agrees well with the prediction of Watson et al. at high masses, but deviates at low masses, perhaps due to our use of a different halo finder or perhaps indicating a break from 'universal' behaviour. We then analyse the dynamical evolution of galaxies during the Epoch of Reionization finding that only a small fraction (~20 per cent) of galactic haloes are relaxed. We illustrate this using standard relaxation metrics to establish two dynamical recovery time-scales: (i) haloes need ~1.5 dynamical times following formation, and (ii) ~2 dynamical times following a major (3:1) or minor (10:1) merger to be relaxed. This is remarkably consistent across a wide mass range. Lastly, we use a phase-space halo finder to illustrate that major mergers drive long-lived massive phase-space structures which take many dynamical times to dissipate. This can yield significant differences in the inferred mass build-up of galactic haloes and we suggest that care must be taken to ensure a physically meaningful match between the galaxy formation physics of semi-analytic models and the halo finders supplying their input.