We give a general analysis of OPEs of 1/2 BPS superfield operators for the D=3,4,5,6 superconformal algebras OSp(8/4,R), PSU(2,2), F_4 and OSp(8^*/4) which underlie maximal AdS supergravity in 4≤ D+1≤ 7. The corresponding three-point functions can be formally factorized in a way similar to the decomposition of a generic superconformal UIR into a product of supersingletons. This allows for a simple derivation of branching rules for primary superfields. The operators of protected conformal

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... on which may appear in the OPE are classified and are shown to be either 1/2 or 1/4 BPS, or semishort. As an application, we discuss the "non-renormalization" of extremal n-point correlators.