  We obtain a ``mean field'' scaling flow of the longitudinal and the Hall
conductivities in the fractional quantum Hall regime. Using the composite
fermion picture and assuming that the composite fermions follow the
Khmelnitskii-Pruisken scaling flow for the integer quantum Hall effect, the
unstable fixed points which govern the transitions between different fractional
quantum Hall states are identified. Distributions of the critical longitudinal
and Hall conductivities at the unstable fixed points are obtained and
implications of the results for the experiments on mesoscopic quantum Hall
systems are discussed.
