  Axions and axion-like particles (ALPs) are some of the most popular
candidates for dark matter, with several viable production scenarios that make
different predictions. In the scenario in which the axion is born after
inflation, its field develops significant inhomogeneity and evolves in a highly
nonlinear fashion. Understanding the eventual abundance and distribution of
axionic dark matter in this scenario therefore requires dedicated numerical
simulations. So far the community has focused its efforts on simulations of the
QCD axion, a model that predicts a specific temperature dependence for the
axion mass. Here, we go beyond the QCD axion, and perform a suite of
simulations over a range of possible temperature dependencies labelled by a
power-law index. We study the complex dynamics of the axion field, including
the scaling of cosmic strings and domain walls, the spectrum of
non-relativistic axions, the lifetime and internal structure of axitons, and
the seeds of miniclusters. In particular, we quantify how much the string-wall
network contributes to the dark matter abundance as a function of how quickly
the axion mass grows. We find that a temperature-independent model produces
25\% more dark matter than the standard misalignment calculation. In contrast
to this generic ALP, QCD axion models are almost six times less efficient at
producing dark matter. Given the flourishing experimental campaign to search
for ALPs, these results have potentially wide implications for direct and
indirect searches.
