  In this paper we consider the unitary symmetric spaces of the form
X=U(p,q)/U(1)U(p,q-1) and their discrete series representations. Inspired by
the work of A.Venkatesh and Y.Sekellarides on L-groups of p-adic spherical
spaces we formulate and prove natural relative branching laws for the
restriction to smaller subgroups of the same type and corresponding unitary
spaces.We think of this as steps to formulation and proving Gan Gross Prasad
conjectures for unitary spaces. Using period integral and some results of
T.Kobayashi we prove an analogue of thesis conjectures.
