  We construct the general static solution to the supergravity action
containing gravity, the dilaton and a set of antisymmetric forms describing the
intersecting branes delocalized in the relative transverse dimensions. The
solution is obtained by reducing the system to a set of separate Liouville
equations (the intersection rules implying the separability); it contains the
maximal number of free parameters corresponding to the rank of the differential
equations. Imposing the requirement of the absence of naked singularities, we
show that the general configurations are restricted to two and only two
classes: the usual asymptotically flat intersecting branes, and the
intersecting branes some of which are asymptotically flat and some approach the
linear dilaton background at infinity. In both cases the configurations are
black. These are supposed to be relevant for the description of the thermal
phase of the QFT's in the corresponding Domain-Wall/QFT duality.
