  Many extensions of the standard model predict the existence of extra neutral
vector bosons, generically referred as $Z^\prime$. This boson may be discovered
at the LHC but in this case it will be necessary to study the respective
parameters in order to discriminate to which model it belongs to. This is a
task for a much clean lepton linear collider as the future ILC. In this paper
we develop an exemplary study of the capability of several asymmetries on and
off $Z^\prime$ peak in discriminating among those extensions with (almost) no
ambiguities.
