International audienceThe hierarchical scenario of structure formation, in the frame of the $Lambda$-CDM cosmology, predicts the existence of dark matter (DM) sub-halos down to very small scales, of which the minimal size depends on the microscopic properties of the DM. In the context of annihilating DM, such substructures are expected to enhance the primary cosmic ray (CR) fluxes originating from DM annihilation in the Galaxy. This enhancement has long been invoked to allow predictions of imprints of DM annihilation on the antimatter CR spectra. Taking advantage of the method developed by Lavalle et al (2007b), we (Lavalle et al, 2007a) accurately compute the boost factors for positrons and anti-protons, as well as the associated theoretic...