  We consider a D-dimensional self-gravitating spherically symmetric
configuration of a generalized electro-magnetic n-form F and a dilatonic scalar
field, admitting an interpretation in terms of intersecting p-branes. For
theories with multiple times, selection rules are obtained, which obstruct the
existence of p-branes in certain subspaces. General static solutions are
obtained under a specific restriction on the model parameters, which
corresponds to the known "intersection rules". More special families of
solutions (with equal charges for some of the F-field components) are found
with weakened restrictions on the input parameters. Black-hole solutions are
determined, and it is shown that in the extreme limit the Hawking temperature
may tend to zero, a finite value, or infinity, depending on the p-brane
intersection dimension. A kind of no-hair theorem is obtained, claiming that
black holes cannot coexist with a quasiscalar component of the F-field.
