We classify the stability region, marginal stability walls (MS) and split
attractor flows for two-center extremal black holes in four-dimensional N=2
supergravity minimally coupled to n vector multiplets. It is found that
two-center (continuous) charge orbits, classified by four duality invariants,
either support a stability region ending on a MS wall or on an anti-marginal
stability (AMS) wall, but not both. Therefore, the scalar manifold never
contains both walls. Moreover, the BPS mass of the black hole composite (in its
stability region) never vanishes in the scalar manifold. For these reasons, the
"bound state transformation walls" phenomenon does not necessarily occur in
these theories. The entropy of the flow trees also satisfies an inequality
which forbids "entropy enigma" decays in these models. Finally, the non-BPS
case, due to the existence of a "fake" superpotential satisfying a triangle
inequality, can be treated as well, and it can be shown to exhibit a split
attractor flow dynamics which, at least in the n=1 case, is analogous to the
BPS one.Comment: 1+29 pages, 2 figures; v2: minor changes, especially in Sects. 1 and
2; Sect. 6 changed. To appear on NP
