  We prove a spanning result for vector-valued Poincar\'e series on a bounded
symmetric domain. We associate a sequence of holomorphic automorphic forms to a
submanifold of the domain. When the domain is the unit ball in ${\Bbb{C}}^n$,
we provide estimates for the norms of these automorphic forms and we find
asymptotics of the norms (as the weight goes to infinity) for a class of
totally real submanifolds. We give an example of a CR submanifold of the ball,
for which the norms of the associated automorphic forms have a different
asymptotic behavior.
