We extend to large transverse momentum p(perpendicular to) an approach to q
uarkonium hadroproduction previously suggested for low p(perpendicular to).
The dynamics involves a perturbative rescattering of the heavy quark pair
off a comoving color field which originates from gluon radiation prior to t
he heavy quark production vertex. Assuming simple properties of the comovin
g held we find the rescattering scenario to be in reasonable agreement with
data. At large p(perpendicular to), psi' is predicted to he unpolarized, a
nd chi (1) production is favored compared to chi (2). We predict the chi (1
) polarization to be transverse at low p(perpendicular to), and to get a lo
ngitudinal component at large p(perpendicular to).