  Dark matter particles could annihilate into light and metastable mediators
subsequently decaying far away from where they are produced. In this scenario,
the indirect signatures of dark matter are altered with respect to the
conventional situation where standard model particles are directly injected
where annihilation happens. We explore here this new phenomenology for which we
devise the tools. We calculate the effective dark matter distribution resulting
from the smearing by mediator propagation. We derive the fluxes of mediators
and their decay particles. We study how the $J$-factor, which naturally appears
in the calculation of the dark matter induced gamma ray signal, is modified in
the presence of mediators. We also derive the anisotropy which the cosmic ray
positron flux exhibits in this scenario. We finally comment upon a recent
proposal based on long-lived mediators where the effective dark matter density
at the Earth is increased such as to explain the cosmic ray positron anomaly.
We conclude that this scenario is barely tenable as regards the very dense dark
matter spike which it requires at the Galactic center. The associated positron
anisotropy is very small and undetectable, except at high energies where it
reaches a level of order $10^{-4}$ to $10^{-3}$.

High Energy Physics - Phenomenology;High Energy Astrophysical Phenomena