  We study a codimension 2 braneworld in the Einstein Gauss-Bonnet gravity. We
carefully examine the structure of possible singularities in the system which
characterize the braneworld through matching conditions. Consequently, we find
that the thickness of the brane can be incorporated as the distributional
source, which we dub quasi-thickness. On the basis of our formalism, we analyze
the linearized gravity and show the conventional Einstein gravity can be
recovered on the brane. In the nonlinear regime, however, we find corrections
due to the thickness and the bulk geometry. We also point out a possibility
that the thickness plays a role of the dark matter/energy in the universe.
