Appendices A and B are only available in electronic form at http://www.aanda.org

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Though those authors have since improved their early time results and parametrisations, we will still use these generic profile names to deal with inner shapes of profiles, for the sake of simplicity.

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...2007)

For further developments on the topic of triaxiality, asymmetries, as well as on the spin of halos, see e.g. Zentner et al. (2005); Gustafsson et al. (2006); Bett et al. (2007); Capuzzo-Dolcetta et al. (2006); Moore et al. (2004); Lee & Kang (2006); Gao & White (2006). For the dependence of halo parameters on the environment, see Ragone-Figueroa & Plionis (2007); Hahn et al. (2007a,b); Maulbetsch et al. (2007).

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... substructures

Small structures, which formed earlier, are expected to be more spherical (Allgood et al. 2006; Moore et al. 2004).

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... $15{-}20\%$

The concentration is modified when considering dark energy with various values of $\omega$ (Dolag et al. 2004), the constant equation of state, but still remains consistent with B01 model (Wechsler et al. 2006).

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...Colafrancesco et al. 2006)

Their figure corresponds to slightly modified B01 and ENS01, which are not retained here.

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... parameters

See discussion in Sect. 3.3 for the consequences of varying $\rho_{\rm sat}$ and considering different inner profiles (e.g. a Moore inner profile).

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... paper

Let us say it again: should the first option have been retained, we would have ended up with boost factors smaller than one!

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... coefficient

So that ${\rm d}N/{\rm d}E\times S\equiv Q(E)$ , as used in Sect. 4.

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... model

This differs from the convention used in Lavalle et al. (2007) for which $(v/4\pi)$ is included in S.

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... uncorrelated

We remind that tidal disruption of a clump in the Galactic centre depends either on its mass and on its location, which induces a small correlation between the mass and the space distributions. Nevertheless, we have checked that it could be neglected for this purpose.

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... distributions)

The integration volume V is the DM halo volume, but in practical calculations, we reduce it to the diffusion volume.

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... flux

An analysis of these effective volumes has been presented and discussed in great details in Maurin & Taillet (2003), for both $\overline {\rm p}$ and ${\rm e}^+$ .

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