  We study both the continuous model and the discrete model of the integer
quantum Hall effect on the hyperbolic plane in the presence of disorder,
extending the results of an earlier paper [CHMM]. Here we model impurities,
that is we consider the effect of a random or almost periodic potential as
opposed to just periodic potentials. The Hall conductance is identified as a
geometric invariant associated to an algebra of observables, which has plateaus
at gaps in extended states of the Hamiltonian. We use the Fredholm modules
defined in [CHMM] to prove the integrality of the Hall conductance in this
case. We also prove that there are always only a finite number of gaps in
extended states of any random discrete Hamiltonian. [CHMM] A. Carey, K.
Hannabuss, V. Mathai and P. McCann, Quantum Hall Effect on the Hyperbolic
Plane, Communications in Mathematical Physics, 190 vol. 3, (1998) 629-673.
