  We measure the anisotropy of dark matter flows on small scales in the near
environment of haloes using a large set of simulations. We rely on two
different approaches to quantify the anisotropy of the cosmic infall: we
measure the flows at the haloes' virial radius while describing the infalling
matter via fluxes through a spherical shell; we measure the spatial and
kinematical distributions of satellites and substructures around haloes
detected by the subclump finder ADAPTAHOP first described in the appendix. The
two methods are found to be in agreement both qualitatively and quantitatively
via one and two points statistics.The infall takes place preferentially in the
plane perpendicular to the direction defined by the halo's spin. We computed
the excess of equatorial accretion both through rings and via a harmonic
expansion of the infall. The level of anisotropy of infalling matter is found
to be ~15 %. The substructures have their spin orthogonal to their velocity
vector in the halo's rest frame at a level of about 5%, suggestive of an image
of a flow along filamentary structures which provides an explanation for the
measured anisotropy. We conclude that a halo does not see its environment as an
isotropic perturbation, investigate how the anisotropy is propagated inwards
using perturbation theory, and discuss briefly implications for weak lensing,
warps and the thickness of galactic disks.
