We explore polarized heavy quarkonium production using the color evaporation
model at leading order. We present the polarized to total yield ratio as a
function of center of mass energy and rapidity in p+p collisions. At energies
far above the QQ production threshold, we find charmonium and
bottomonium production to be longitudinally polarized (Jz=0). The quarkonium
states are also longitudinally polarized at central rapidity, becoming
transversely polarized (Jz=±1) at the most forward rapidities