  The PHENIX collaboration presents a systematic study of $\pi^0$ production
from $p$$+$$p$, $p$$+$Al, $p$$+$Au, $d$$+$Au, and $^{3}$He$+$Au collisions at
$\sqrt{s_{_{NN}}}=200$ GeV. Measurements were performed with different
centrality selections as well as the total inelastic, 0%--100%, selection for
all collision systems. For 0%--100% collisions, the nuclear modification
factors, $R_{xA}$, are consistent with unity for $p_T$ above 8 GeV/$c$, but
exhibit an enhancement in peripheral collisions and a suppression in central
collisions. The enhancement and suppression characteristics are similar for all
systems for the same centrality class. It is shown that for high-$p_T$-$\pi^0$
production, the nucleons in the $d$ and $^3$He interact mostly independently
with the Au nucleus and that the counter intuitive centrality dependence is
likely due to a physical correlation between multiplicity and the presence of a
hard scattering process. These observations disfavor models where parton energy
loss has a significant contribution to nuclear modifications in small systems.
Nuclear modifications at lower $p_T$ resemble the Cronin effect -- an increase
followed by a peak in central or inelastic collisions and a plateau in
peripheral collisions. The peak height has a characteristic ordering by system
size as $p$$+$Au $>$ $d$$+$Au $>$ $^{3}$He$+$Au $>$ $p$$+$Al. For collisions
with Au ions, current calculations based on initial state cold nuclear matter
effects result in the opposite order, suggesting the presence of other
contributions to nuclear modifications, in particular at lower $p_T$.
