  We investigate the effects of dephasing on the current statistics of
mesoscopic conductors with a recently developed statistical model, focusing in
particular on mesoscopic cavities and Aharonov-Bohm rings. For such devices, we
analyze the influence of an arbitrary degree of decoherence on the cumulants of
the current. We recover known results for the limiting cases of fully coherent
and totally incoherent transport and are able to obtain detailed information on
the intermediate regime of partial coherence for a varying number of open
channels. We show that dephasing affects the average current, shot noise, and
higher order cumulants in a quantitatively and qualitatively similar way, and
that consequently shot noise or higher order cumulants of the current do not
provide information on decoherence additional or complementary to what can be
already obtained from the average current.
