  We have recently introduced a novel statistical measure of dark matter
clustering in phase space, the particle phase space average density ($P^2SAD$).
In a two-paper series, we studied the structure of $P^2SAD$ in the
Milky-Way-size Aquarius haloes, constructed a physically motivated model to
describe it, and illustrated its potential as a powerful tool to predict
signals sensitive to the nanostructure of dark matter haloes. In this letter,
we report a remarkable universality of the clustering of dark matter in phase
space as measured by $P^2SAD$ within the subhaloes of host haloes across
different environments covering a range from dwarf-size to cluster-size haloes
($10^{10}-10^{15}$ M$_\odot$). Simulations show that the universality of
$P^2SAD$ holds for more than 7 orders of magnitude, over a 2D phase space,
covering over 3 orders of magnitude in distance/velocity, with a simple
functional form that can be described by our model. Invoking the universality
of $P^2SAD$, we can accurately predict the non-linear power spectrum of dark
matter at small scales all the way down to the decoupling mass limit of cold
dark matter particles. As an application, we compute the subhalo boost to the
annihilation of dark matter in a wide range of host halo masses.
