  The transport properties of a rectangular mesoscopic plaquette in the
presence of a perpendicular magnetic field are studied in a tight-binding model
with randomly distributed traps. The longitudinal and Hall resistances are
calculted in the four-probe Landauer-B\"{u}ttiker formalism which accounts
automatically both for the quantum coherence and the trapping-induced
localization. The localized character of eigenvectors and the specific aspect
of the density of states at a given magnetic flux are correlated with the
behaviour of the mentioned resistances as function of the Fermi energy. The
Hall insulator and quantum Hall regimes are evidentiated. The dependence on
magnetic field of the configurational averages of the longitudinal and Halll
resistance is studied in a purely quantum-mechanical approach. Both negative
and positive magnetoresistances are found.
