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We investigate the cosmology of mini Primordial Black Holes (PBHs) producedby large density perturbations. The mini PBHs evaporate promptly in the earlyuniverse and we assume that a stable remnant is left behind. The PBHs remnantscan constitute the entire dark matter of the universe for a wide range ofremnant masses. We build inflationary models, in the framework of$\alpha$-attractors utilizing exponential functions, in which the PBHs areproduced during matter, radiation and kination domination eras. The advantageof these inflationary models is that the spectral index takes values favorableby the Planck 2018 data. The PBH production from runaway inflaton models hasthe unique and very attractive feature to automatically reheat the universe. Inthese models the PBHs are produced during the kination stage and their promptevaporation efficiently produces the required entropy.  Such runaway models are remarkably economic having interesting implicationsfor the early universe cosmology, possibly giving rise to a wCDM late timecosmology as well.

PBH remnants as dark matter produced in thermal, matter and runaway-quintessence post-inflationary scenarios