  We apply the entropy formalism to the study of the near-horizon geometry of
extremal black p-brane intersections in D>5 dimensional supergravities. The
scalar flow towards the horizon is described in terms an effective potential
given by the superposition of the kinetic energies of all the forms under which
the brane is charged. At the horizon active scalars get fixed to the minima of
the effective potential and the entropy function is given in terms of U-duality
invariants built entirely out of the black p-brane charges. The resulting
entropy function reproduces the central charges of the dual boundary CFT and
gives rise to a Bekenstein-Hawking like area law. The results are illustrated
in the case of black holes and black string intersections in D=6, 7, 8
supergravities where the effective potentials, attractor equations, moduli
spaces and entropy/central charges are worked out in full detail.
