  If dark matter is an axion-like-particle a significant fraction of the
present day relic abundance could be concentrated in compact gravitationally
bound miniclusters. We study the minicluster masses compatible with the dark
matter relic density constraint. If they form from fluctuations produced by PQ
symmetry breaking, minicluster masses up to hundreds of solar masses are
possible, although over most of the parameter space they are much lighter. The
size of these objects is typically within a few orders of magnitude of an
astronomical unit. We also show that miniclusters can form if an axion gets
mass from a hidden sector with a first order phase transition that takes a
relatively long time to complete. Therefore they can appear in models where PQ
symmetry is broken before inflation, compatible with large axion decay
constants and string theory UV completions.
