  We show that if dark matter consists of QCD axions in the post-inflationary
scenario more than ten percent of it efficiently collapses into Bose stars at
matter-radiation equality. Such a result is mostly independent of the present
uncertainties on the axion mass. This large population of solitons, with
asteroid masses and Earth-Moon distance sizes, might plausibly survive until
today, with potentially interesting implications for phenomenology and
experimental searches.
