  Thickness corrections to static, axisymmetric Dirac-Nambu-Goto branes
embedded into spherically symmetric black hole spacetimes with arbitrary number
of dimensions are studied. First, by applying a perturbative approximation, it
is found that the thick solutions deviate significantly in their analytic
properties from the thin ones near the axis of the system, and perturbative
approaches around the thin configurations can not provide regular thick
solutions above a certain dimension. For the general case, a non-perturbative,
numerical approach is applied and regular solutions are obtained for arbitrary
brane and bulk dimensions. As a special case, it has been found that
2-dimensional branes are exceptional, as they share their analytic properties
with the thin branes rather than the thick solutions of all other dimensions.
