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Axion stars are highly overdense condensates of axion dark matter that can lead to a range of observable phenomena such as resonant emission of radio photons and relativistic axion bursts. Based on simulations of wave dark matter, axion stars are expected to appear abundantly as the solitonic cores of axion miniclusters. We infer the estimated properties and mass distribution of axion stars in our galaxy from analytical predictions of the minicluster mass distribution at present-day redshift. Applying our results to different signatures of axion small-scale structure, we find that neutron star collisions are unlikely to yield sufficient signal rates, while Bosenovae and radio bursts from minicluster mergers can occur as often as ~10/yr/galaxy. We also suggest a new emission mechanism involving the resonant radio conversion of dark matter in accreting axion stars.