If primordial black holes (PBHs) had come to dominate the energy density of the early Universe when oscillations in the axion field began, we show that the relic abundance and expected mass range of the QCD axion would be greatly modified. Since the QCD axion is a potential candidate for dark matter (DM), we refer to it as the DM axion. We predominantly explore PBHs in the mass range (106 - 5× 108)g. We investigate the relation between the relic abundance of DM axions and the parameter space of PBHs. We numerically solve the set of Boltzmann equations, that governs the cosmological evolution during both radiation and PBH-dominated epochs, providing the bulk energy content of the early Universe. We further solve the equation of motion of the DM axion field to obtain its present abundance. Alongside non-relativistic production mechanisms, light QCD axions are generated from evaporating PBHs through the Hawking mechanism and could make up a fraction of the dark radiation (DR). If the QCD axion is ever discovered, it will give us insight into the early Universe and probe into the physics of the PBH-dominated era. We estimate the bounds on the model from DR axions produced via PBH evaporation and thermal decoupling, and we account for isocurvature bounds for the period of inflation where the Peccei-Quinn symmetry is broken. We assess the results obtained against the available CMB data and we comment on the forecasts from gravitational wave searches. We briefly state the consequences of PBH accretion and the uncertainties this may further add to cosmology and astroparticle physics modeling.

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