  We study the matching conditions of intersecting brane worlds in Lovelock
gravity in arbitrary dimension. We show that intersecting various codimension 1
and/or codimension 2 branes one can find solutions that represent
energy-momentum densities localized in the intersection, providing thus the
first examples of infinitesimally thin higher codimension braneworlds that are
free of singularities and where the backreaction of the brane in the background
is fully taken into account.
