Topological Anderson transitions, which are direct phase transitions between topologically distinct Anderson localized phases, allow for criticality in one-dimensional disordered systems. We analyze the statistical properties of an ensemble of critical wave functions at such transitions. We find that the local moments are strongly inhomogeneous, with significant amplification towards the edges of the system. In particular, we obtain an analytic expression for the spatial profile of the local moments, which is valid at all topological Anderson transitions in one dimension, as we verify by direct comparison with numerical simulations of various lattice models
