  Topological Anderson transitions, which are direct phase transitions between
topologically distinct Anderson localised phases, allow for criticality in 1D
disordered systems. We analyse the statistical properties of an emsemble of
critical wavefunctions 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
1D, as we verify by direct comparison with numerical simulations of various
lattice models.
