  We study the spin texture of a generic helical liquid, the edge modes of a
two-dimensional topological insulator with broken axial spin-symmetry. By
considering honeycomb and square lattice realizations of topological
insulators, we show that in all cases the generic behavior of a
momentum-dependent rotation of the spin quantization axis is realized. Here we
establish this mechanism also for disk geometries with continuous rotational
symmetry. Finally, we demonstrate that the rotation of spin-quantization axis
remains intact for arbitrary geometries, i.e. in the absence of any continuous
symmetry. We also calculate the dependence of this rotation on the model and
material parameters. Finally we propose a spectroscopy measurement which should
directly reveal the rotation of the spin-quantization axis of the helical edge
states.
