  The quantum Hall effects in the sliding bilayer graphene and AAB-stacked
trilayer system are investigated by the Kubo formula and the generalized
tight-binding model. The various stacking configurations can greatly diversify
the magnetic quantization and thus create the rich and unique transport
properties. The quantum conductivities are very sensitive to the Fermi energy
and magnetic-field strength. The diverse features cover the specific
non-integer conductivities, the integer conductivities with the distinct steps,
the splitting-created reduction and complexity of quantum conductivity, a
vanishing or non-zero conductivity at the neutral point, and the well-like,
staircase, composite, and abnormal plateau structures in the
field-dependencies. Such stacking-dependent characteristics mainly originate
from the crossing, anticrossing and splitting Landau-level energy spectra and
three kinds of quantized modes.
