  We perform a general analysis of representations of the superconformal
algebras OSp(8/4,R) and OSp(8*/2N) in harmonic superspace. We present a
construction of their highest-weight UIR's by multiplication of the different
types of massless conformal superfields ("supersingletons"). In particular, all
"short multiplets" are classified. Representations undergoing shortening have
"protected dimension" and may correspond to BPS states in the dual supergravity
theory in anti-de Sitter space. These results are relevant for the
classification of multitrace operators in boundary conformally invariant
theories as well as for the classification of AdS black holes preserving
different fractions of supersymmetry.
