  Using the Millennium N-body simulation we explore how the shape and angular
momentum of galaxy dark matter haloes surrounding the largest cosmological
voids are oriented. We find that the major and intermediate axes of the haloes
tend to lie parallel to the surface of the voids, whereas the minor axis points
preferentially in the radial direction. We have quantified the strength of
these alignments at different radial distances from the void centres. The
effect of these orientations is still detected at distances as large as 2.2
R_void from the void centre. Taking a subsample of haloes expected to contain
disc-dominated galaxies at their centres we detect, at the 99.9% confidence
level, a signal that the angular momentum of those haloes tends to lie parallel
to the surface of the voids. Contrary to the alignments of the inertia axes,
this signal is only detected in shells at the void surface (1<R<1.07 R_void)
and disappears at larger distances. This signal, together with the similar
alignment observed using real spiral galaxies (Trujillo, Carretero & Patiri
2006), strongly supports the prediction of the Tidal Torque theory that both
dark matter haloes and baryonic matter have acquired, conjointly, their angular
momentum before the moment of turnaround.
