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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${}_4$ andOSp($8^*/4$) which underlie maximal AdS supergravity in $4\leq D+1\leq 7$. \\The corresponding three-point functions can be formally factorized in a waysimilar to the decomposition of a generic superconformal UIR into a product ofsupersingletons. This allows for a simple derivation of branching rules forprimary superfields. The operators of protected conformal dimension which mayappear in the OPE are classified and are shown to be either 1/2 or 1/4 BPS, orsemishort. As an application, we discuss the "non-renormalization" of extremal$n$-point correlators.Comment: To be published in NJP Focus Issue: Supersymmetry in condensed matter  and high energy physic

Universal properties of superconformal OPEs for 1/2 BPS operators in3⩽D⩽6