  We carry out a general analysis of the representations of the superconformal
algebras OSp(8/4,R) and OSp(8*/2N) in terms of harmonic superspace. We present
a construction of their highest-weight UIR's by multiplication of the different
types of massless conformal superfields ("supersingletons"). Particular
attention is paid to the so-called "short multiplets". 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.
