  We show that the Lovelock type brane gravity is naturally holographic by
providing a correspondence between bulk and surface terms that appear in the
Lovelock-type brane gravity action functional. We prove the existence of
relationships between the $\mathcal{L}_{\mbox{\tiny bulk}}$ and
$\mathcal{L}_{\mbox{\tiny surf}}$ allowing $\mathcal{L}_{\mbox{\tiny surf}}$ to
be determined completely by $\mathcal{L}_{\mbox{\tiny bulk}}$. In the same
spirit, we provide relationships among the various conserved tensors that this
theory possesses. We further comment briefly on the correspondence between
geometric degrees of freedom in both bulk and surface space.
