  We study how the evaporation of primordial black holes (PBHs) can affect the
production of dark matter (DM) particles through thermal processes. We consider
fermionic DM interacting with Standard Model particles via a spin-1 mediator in
the context of a Freeze-Out or Freeze-In mechanism. We show that when PBHs
evaporate after dominating the Universe's energy density, PBHs act as a source
of DM and continuously inject entropy into the visible sector that can affect
the thermal production in three qualitatively different ways. We compute the
annihilation cross-sections which account for the interactions between and
within the PBH produced and thermally produced DM populations, and establish a
set of Boltzmann equations which we solve to obtain the correct relic abundance
in those different regimes and confront the results with a set of different
cosmological constraints. We provide analytic formulae to calculate the relic
abundance for the Freeze-Out and Freeze-In mechanism in a PBH dominated early
Universe. We identify regions of the parameter space where the PBHs dilute the
relic density and thermalization occurs. Furthermore, we have made our code
that numerically solves the Boltzmann equations publicly available.
