  Using a high resolution DM simulation of the Local Group (LG), conducted
within the framework of the Constrained Local UniversE Simulation (CLUES)
project, we investigate the nature of how satellites of the MW and M31 are
accreted. Satellites of these galaxies are accreted anisotropically, entering
the virial radius of their hosts from specific "spots" with respect to the
large scale structure. Furthermore, material which is tidally stripped from
these satellites is also, at z=0, distributed anisotropically and is
characterized by an ellipsoidal sub-volume embedded in the halo. The angular
pattern created by the locus of satellite infall points and the projected
stripped DM is investigated within a coordinate system determined by the
location of the LG companion and the simulated Virgo cluster across concentric
shells ranging from 0.1 to 5 r_vir. Remarkably, the principal axis of the
ellipsoidal sub-volume shows a coherent alignment extending from well within
the halo to a few r_vir. A spherical harmonics transform applied to the angular
distributions confirms the visual impression: namely, the angular distributions
of both the satellites entry points and stripped DM is dominated by the l=2
quadrupole term, whose major principal axis is aligned across the shells
considered. It follows that the structure of the outer (r>0.5 r_vir) regions of
the main halos is closely related to the cosmic web within which it is
embedded. Given the hypothesis that a large fraction of the stellar halo of the
Milky Way has been accreted from satellites, the present results can be applied
to the stellar halo of the MW and M31. We predict that the remnants of tidally
stripped satellites should be embedded in streams of material composed of dark
matter and stars. The present results can therefore shed light on the existence
of satellites embedded within larger streams of matter, such as the Segue 2
satellite.
