  We analyze in detail the renormalization group flows which follow from the
recently proposed all orders beta functions for the Chalker-Coddington network
model. The flows in the physical regime reach a true singularity after a finite
scale transformation. Other flows are regular and we identify the asymptotic
directions. One direction is in the same universality class as the disordered
XY model.
  The all orders beta function is computed for the network model of the spin
Quantum Hall transition and the flows are shown to have similar properties. It
is argued that fixed points of general current-current interactions in 2d
should correspond to solutions of the Virasoro master equation. Based on this
we identify two coset conformal field theories osp(2N|2N)_1 /u(1)_0 and
osp(4N|4N)_1/su(2)_0 as possible fixed points and study the resulting
multifractal properties. We also obtain a scaling relation between the typical
amplitude exponent alpha_0 and the typical point contact conductance exponent
X_t which is expected to hold when the density of states is constant.
