We carry out a general analysis of the representations of the superconforma
l algebras SU(2, 2/N), OSp(8/4, R), and OSp(8*/2N) and give their realizati
on in superspace. We present a construction of their UIRs by multiplication
of the different types of massless superfields ("supersingletons"). Partic
ular 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 resu
lts are relevant for the classification of multitrace operators in boundary
conformally invariant theories as well as for the classification of AdS bl
ack holes preserving different fractions of supersymmetry.