  We study effects of disorder on the integer quantized Hall effect within the
screening theory, systematically. The disorder potential is analyzed
considering the range of the potential fluctuations. Short range part of the
single impurity potential is used to define the conductivity tensor elements
within the self-consistent Born approximation, whereas the long range part is
treated self-consistently at the Hartree level. Using the simple, however,
fundamental Thomas-Fermi screening, we find that the long range disorder
potential is well screened. While, the short range part is approximately
unaffected by screening and is suitable to define the mobility at vanishing
magnetic fields. In light of these range dependencies we discuss the extend of
the quantized Hall plateaus considering the "mobility" of the wafer and the
width of the sample, by re-formulating the Ohm's law at low temperatures and
high magnetic fields. We find that, the plateau widths mainly depend on the
long range fluctuations of the disorder, whereas the importance of density of
states broadening is less pronounced and even is predominantly suppressed.
These results are in strong contrast with the conventional single particle
pictures. We show that the widths of the quantized Hall plateaus increase with
increasing disorder, whereas the level broadening is negligible.
