  We demonstrate that the $p_T$ dependence of the $\eta/\pi^0$ ratio is
universal within a few percent for high energy $p$+$p$, $p$+A and $d$+A
collisions, over a broad range of collision energies. The $\eta/\pi^0$ ratio
increases with $p_T$ up to 4 to 5 GeV/$c$ where it saturates at a nearly
constant value of 0.487$\pm$0.024. Above $p_T = 5$ GeV/$c$ the same constant
value is also observed in A+A collisions independent of collision system,
energy, and centrality. At lower $p_T$, where accurate $\eta/\pi^0$ data is
absent for A+A collisions, we estimate possible deviations from the universal
behavior, which could arise due to the rapid radial hydrodynamic expansion of
the A+A collision system. For A+A collisions at RHIC we find that possible
deviations are limited to the $p_T$ range from 0.4 to 3 GeV/$c$, and remain
less than 20% for the most central collisions.
