  The direct detection of dark matter on Earth depends crucially on its density
and its velocity distribution on a milliparsec scale. Conventional N-body
simulations are unable to access this scale, making the development of other
approaches necessary. In this paper, we apply the method developed in Fantin et
al. 2008 to a cosmologically-based merger tree, transforming it into a useful
instrument to reproduce and analyse the merger history of a Milky Way-like
system. The aim of the model is to investigate the implications of any
ultra-fine structure for the current and next generation of directional dark
matter detectors. We find that the velocity distribution of a Milky Way-like
Galaxy is almost smooth, due to the overlap of many streams of particles
generated by multiple mergers. Only the merger of a 10^10 Msun analyse can
generate significant features in the ultra-local velocity distribution,
detectable at the resolution attainable by current experiments.
