  The complete phase diagram of objects in M-theory compactified on tori $T^p$,
$p=1,2,3$, is elaborated. Phase transitions occur when the object localizes on
cycle(s) (the Gregory-Laflamme transition), or when the area of the localized
part of the horizon becomes one in string units (the Horowitz-Polchinski
correspondence point). The low-energy, near-horizon geometry that governs a
given phase can match onto a variety of asymptotic regimes. The analysis makes
it clear that the matrix conjecture is a special case of the Maldacena
conjecture.
