  We present a numerical solution for a topologically flat 2-dimensional thick
brane on a higher dimensional, spherically symmetric black hole background.
Present solution is the last, missing part of the complete set of solutions for
the thickness corrected brane-black hole problem in arbitrary number of
dimensions. We show that the 2-dimensional case is special compared to all the
higher dimensional solutions in the topologically Minkowskian family as being
non-analytic at the axis of the system. We provide the numerical solution in
the near horizon region and make a comparison with the infinitely thin case.
