  We present a Monte Carlo (MC) study of $W^{\pm}$ and $Z_{0}$ production of
longitudinally polarized proton collisions at a center of mass (CMS) energy of
$500\,{\rm GeV}$. All results were obtained with the SPHINX MC code. We
consider two different types of polarized parton distributions with large and
small gluon polarization. Various spin asymmetries are found to be sensitive to
the shape of the polarized gluon distribution between
$0.1\stackrel{<}{\sim}x\stackrel{<}{\sim}0.5$. The asymmetries are
approximately constant with respect to the transverse momentum carried by the
$W^{\pm}$ and $Z_{0}$, {\em except} if the first moment of the gluon
polarization is large. In this case some $W^{\pm}$ asymmetries show a
significant variation with transverse momentum.
