  We investigate the effects of producing dark matter by Hawking evaporation of
primordial black holes (PBHs) in scenarios that may have a second
well-motivated dark matter production mechanism, such as freeze-out, freeze-in,
or gravitational production. We show that the interplay between PBHs and the
alternative sources of dark matter can give rise to model-independent
modifications to the required dark matter abundance from each production
mechanism, which in turn affect the prospects for dark matter detection. In
particular, we demonstrate that for the freeze-out mechanism, accounting for
evaporation of PBHs after freeze-out demands a larger annihilation cross
section of dark matter particles than its canonical value for a thermal dark
matter. For mechanisms lacking thermalization due to a feeble coupling to the
thermal bath, we show that the PBH contribution to the dark matter abundance
leads to the requirement of an even feebler coupling. Moreover, we show that
when a large initial abundance of PBHs causes an early matter-dominated epoch,
PBH evaporation alone cannot explain the whole abundance of dark matter today.
In this case, an additional production mechanism is required, in contrast to
the case when PBHs are formed and evaporate during a radiation-dominated epoch.
