  Should Primordial Black Holes (PBHs) exist in nature, they would inevitably
accrete baryonic matter in their vicinity. In turn, the consequent emission of
high-energy radiation could affect the thermal history of the universe to an
extent that can be probed with a number of cosmological observables such as the
Cosmic Microwave Background (CMB) anisotropies. However, our understanding of
the accretion and radiation emission processes in the context of PBHs is still
in its infancy, and very large theoretical uncertainties affect the resulting
constraints on the PBH abundance. Building on state-of-the-art literature, in
this work we take a step towards the development of a more realistic picture of
PBH accretion by accounting for the contribution of outflows. Specifically, we
derive CMB-driven constraints on the PBH abundance for various accretion
geometries, ionization models and mass distributions in absence and in presence
of mechanical feedback and non-thermal emissions due to the outflows. As a
result, we show that the presence of such outflows introduces an additional
layer of uncertainty that needs to be taken into account when quoting
cosmological constraints on the PBH abundance, with important consequences in
particular in the LIGO-Virgo-KAGRA observational window.
