  [Abridged]. We take advantage of the galaxy-like 3D dark matter map extracted
from the HORIZON Project results to calculate the positron and antiproton
fluxes from dark matter annihilation, in a model-independent approach as well
as for dark matter particle benchmarks relevant at the LHC scale (from
supersymmetric and extra-dimensional theories). Such a study is dedicated to a
better estimate of the theoretical uncertainties affecting predictions, while
the PAMELA and GLAST satellites are currently taking data which will soon
provide better observational constraints. We discuss the predictions of the
antiproton and positron fluxes, and of the positron fraction as well, as
compared to the current data. We finally discuss the limits of the Nbody
framework in describing the dark matter halo of our Galaxy.
