  We present an analytic theory of quantum criticality in quasi one-dimensional
topological Anderson insulators. We describe these systems in terms of two
parameters $(g,\chi)$ representing localization and topological properties,
respectively. Certain critical values of $\chi$ (half-integer for $\Bbb{Z}$
classes, or zero for $\Bbb{Z}_2$ classes) define phase boundaries between
distinct topological sectors. Upon increasing system size, the two parameters
exhibit flow similar to the celebrated two parameter flow of the integer
quantum Hall insulator. However, unlike the quantum Hall system, an exact
analytical description of the entire phase diagram can be given in terms of the
transfer-matrix solution of corresponding supersymmetric non-linear
sigma-models. In $\Bbb{Z}_2$ classes we uncover a hidden supersymmetry, present
at the quantum critical point.
