  We predict Anderson localization of light with nested screw topological
dislocations propagating in disordered two-dimensional arrays of hollow
waveguides illuminated by vortex beams. The phenomenon manifests itself in the
statistical presence of topological dislocations in ensemble-averaged output
distributions accompanying standard disorder-induced localization of light
spots. Remarkably, screw dislocations are captured by the light spots despite
the fast and irregular transverse displacements and topological charge flipping
undertaken by the dislocations due to the disorder. The statistical averaged
modulus of the output local topological charge depends on the initial vorticity
carried by the beam.
