In this article we aim to provide a principled analysis of a complex of phenomena concerning the way the possession relation is manifested and its morpho-syntactic expression. We will focus on the possessive structures of Aromanian varieties spoken in Southern Albania, the Rëmen of Libofshë (Fier) and Vlleht of Këllez (Gjirokastër), where possessives follow the head noun with which they agree and are preceded by the invariable Possessive introducer (PI) a both within DPs and in predicative contexts. The comparison with Albanian and Southern Italian possessives inspires a lexicalist approach where variation stems from the interplay between different morpho-lexical tools and the universal basic combinatory mechanism (Chomsky 2005). We consider the following phenomena: (i) The nature of a in Aromanian possessives and the structure of possessive; (ii) Genitive and linker-like elements: di in Calabrian, pre-adjectival article in Albanian; (iii) Kinship terms possessives with enclitic position in Aromanian and Southern Italian dialects. The conceptual constraints shaping the possessive systems are based on categorial properties regarding the nominal domain: (differential) lexicalization of the -features of DP, 1st/2nd/3rd singular vs plural, kinship terms vs other nouns, linearization of semantic relations and externalization.