  We use a modified version of the Peak Patch excursion set formalism to
compute the mass and size distribution of QCD axion miniclusters from a fully
non-Gaussian initial density field obtained from numerical simulations of axion
string decay. We find strong agreement with N-Body simulations at a
significantly lower computational cost. We employ a spherical collapse model
and provide fitting functions for the modified barrier in the radiation era.
The halo mass function at $z=629$ has a power-law distribution $M^{-0.6}$ for
masses within the range $10^{-15}\lesssim M\lesssim 10^{-10}M_{\odot}$, with
all masses scaling as $(m_a/50\mu\mathrm{eV})^{-0.5}$. We construct merger
trees to estimate the collapse redshift and concentration mass relation,
$C(M)$, which is well described using analytical results from the initial power
spectrum and linear growth. Using the calibrated analytic results to
extrapolate to $z=0$, our method predicts a mean concentration $C\sim
\mathcal{O}(\text{few})\times10^4$. The low computational cost of our method
makes future investigation of the statistics of rare, dense miniclusters easy
to achieve.
