  The main result of this paper is a sufficient condition in order to have a
compact Thom-Mather stratified pseudomanifold endowed with a $\hat{c}$-iterated
edge metric on its regular part $q$-parabolic. Moreover, besides stratified
pseudomanifolds, the $q$-parabolicity of other classes of singular spaces, such
as compact complex Hermitian spaces, is investigated.
