We have studied magnetotransport in diffusive submicron wires ( (\mathrm{n}^{+}-\mathrm{GaAs}) ) at high magnetic fields where (\omega_{c} \tau>1). The system allowed us to follow a transition from orthodox mesoscopic behaviour to the regime of edge state transpor.
We found that for (\omega_{\mathrm{c}} \tau>1) the universal conductance fluctuations (UCF) can no longer be scaled in terms of only one parameter, the phase coherence length. This breakdown of universal scaling is seen as a large increase of the Lee-Stone correlation field while the magnitude of UCF is unchanged in strong disagreement with the theoretical prediction.
A qualitatively new magnetoresistance oscillatory effect has been observed at intermediate temperatures ((10 \mathrm{~K}<\mathrm{T}<50 \mathrm{~K})) when the quantum transport along the edges coexists with classical (diffusive and dissipative) conduction in the bulk. The effect arises due to Landau quantization but entirely disappears at low temperatures. The latter distinguishes it from the other quantum transport phenomena and indicates the importance of dissipation in resistance measurement.