Universal properties of superconformal OPEs for 1/2 BPS operators in 3 ≤ D ≤ 6

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, 2/4), F-4 and OSp (8*/4) which underlie maximal AdS supergravity in 4 less than or equal toD + 1 less than or equal to 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 dimension 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.