  The sensitivity to the $Z^\prime$ couplings of the processes $e^+e^-\to
l^+l^-,\bar{b}b$ and $\bar{c}c$ at the linear collider with $\sqrt{s}=500 GeV$
with initial beam polarization, for typical extended model examples are
studied. To this aim, the suitable integrated, polarized, observables directly
related to the helicity cross sections that carry information on the individual
$Z^\prime$ chiral couplings to fermions are used. We discuss the derivation of
separate, model-independent limits on the couplings in the case of no observed
indirect $Z^\prime$ signal within the expected experimental accuracy. In the
hypothesis that such signals were, indeed, observed we assess the expected
accuracy on the numerical determination of such couplings and the consequent
range of $Z^\prime$ masses where the individual models can be distinguished
from each other as the source of the effect.
