We calculate the critical power for collapse of linearly-polarized phase vortices, and show that this expression is more accurate than previous results. Unlike the non-vortex case, deviations from radial symmetry do not increase the critical power for collapse, but rather lead to disintegration into collapsing non-vortex filaments. The cases of circular, radial and azimuthal polarizations are
... [Show full abstract] also considered.