  We summarize the screening theory of the integer quantized Hall effect (IQHE)
and emphasize its two key mechanisms: first, the existence, in certain magnetic
field intervals, of incompressible strips, with integer values of the local
filling factor and quantized values of longitudinal and Hall resistivity, and
second, the confinement of an imposed dissipative current to these strips,
leading to the quantization of the global resistances. We demonstrate that,
without any localization assumption, this theory explains the enormous
experimental reproducibility of the quantized resistance values, as well as
experimental results on the potential distribution in narrow Hall bars. We
further demonstrate that inclusion of long-range potential fluctuations allows
to apply the theory to wider Hall bars, and can lead to a broadening of the
quantum Hall plateaus, whereas short-range disorder tends to narrow the
plateaus.
