  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 $4\leq D+1\leq 7$. \\
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.
