This paper deals with a historical shift in the semantics and morpho-syntax of pre-nominal possessives in Romance languages. Empirically, their evolution follows one of the two main diachronic paths: they either stop co-occurring with determiners (French, Spanish) or, else, start requiring their presence (Portuguese, Italian). Contrary to the common view which associates the first case with a transition from a modifier to a determiner semantics and the second with a retention of a modifier semantics (e.g. Alexiadou 2004), we propose that there is a common semantico-syntactic shift underlying both patterns, the rise of an innovative grammar which parses noun phrases with possessives as relational determiner phrases. The surface difference is accounted for by differences in what role a possessive plays in the spellout: either it serves as an exponent of D in the context of a relational component R (the first group) or as an exponent of R itself (the second group). We argue that this shift is part of a more general switch to a D-grammar, which happens as a consequence of an emerging pressure to morphologically mark existential presupposition at the noun phrase level. The more general change independently manifests itself as the overall rise in the frequency of determiners. On the basis of datasets from historical treebanks of French, Spanish, Portuguese, and Italian, we compare rates of change in possessive patterns, as well rates of the rise of determiner frequency across Romance.