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In this paper, we study eight asynchronous communication primitives, arising from the combination of three features: arity (monadic vs polyadic data), communication medium (message passing vs shared dataspaces) and pattern-matching. Each primitive has been already used in at least one language appeared in literature; however, to uniformly reason on such primitives, we plugged them in a common framework inspired by the asynchronous π-calculus. By means of possibility/impossibility of ‘reasonable' encodings, we compare every pair of primitives to obtain a hierarchy of languages based on their relative expressive power.