  We investigate the production of QCD axion dark matter in a nonstandard
cosmological era triggered by primordial black holes (PBHs) that fully
evaporate before the onset of BBN. Even if PBHs cannot emit the whole axion
cold dark matter abundance through Hawking radiation, they can have a strong
impact on the dark matter produced via the misalignment mechanism. First, the
oscillation temperature of axions reduces if there is a PBH dominated era, and
second, PBH evaporation injects entropy to the standard model, diluting the
axion relic abundance originally produced. The axion window is therefore
enlarged, reaching masses as light as $\sim 10^{-8}$ eV and decay constants as
large as $f_{a}\sim 10^{14}$ GeV without fine tuning the misalignment angle.
Such small masses are in the reach of future detectors as ABRACADABRA, KLASH,
and ADMX, if the axion couples to photons. Additionally, the axions radiated by
PBHs contribute to $\Delta N_\text{eff}$ within the projected reach of the
future CMB Stage 4 experiment.
