Given a complex simply connected simple algebraic group G of exceptional type and a maximal parabolic subgroup P of G, we classify all triples (G,P,H) such
that H is a maximal reductive subgroup of G acting spherically on G/P .
In addition we derive branching rules for the restriction of the simple G-modules V(k\omega_i)* to H, where k \in N and \omega_i is the fundamental weight associated to P. Further we find the combinatorial invariants for the spherical affine cones over G/P
