Primordial black holes may have been produced in the early stages of the thermal history of the Universe after cosmic inflation. If so, dark matter in the form of elementary particles can be subsequently accreted around these objects, in particular when it gets non-relativistic and further streams freely in the primordial plasma. A dark matter mini-spike builds up gradually around each black hole, with density orders of magnitude larger than the cosmological one. We improve upon previous work by carefully inspecting the computation of the mini-spike radial profile as a function of black hole mass, dark matter particle mass and temperature of kinetic decoupling. We identify a phase-space contribution that has been overlooked and that leads to changes in the final results. We also derive complementary analytical formulae using convenient asymptotic regimes, which allows us to bring out peculiar power-law behaviors for which we provide tentative physical explanations.

Galactic charged cosmic rays (notably electrons, positrons, antiprotons and light antinuclei) are powerful probes of dark matter annihilation or decay, in particular for candidates heavier than a few MeV or tiny evaporating primordial black holes. Recent measurements by e.g. PAMELA, AMS-02 or Voyager on positrons and antiprotons already translate into constraints on several models over a large mass range. However, these constraints depend on galactic transport models, in particular the diffusive halo size, subject to theoretical and statistical uncertainties. We update the so-called MIN-MED-MAX benchmark transport parameters that yield generic minimal, median and maximal dark-matter produced fluxes; this reduces the uncertainties on fluxes by a factor of about 2 with respect to their former version. We also provide handy fitting formulae for the associated predicted secondary antiproton and positron background fluxes. Finally, for more refined analyses, we provide the full details of the model parameters and covariance matrix of uncertainties.