The aim of this paper is to provide a unified analysis of partitive constructions like one/some of the boxes which, unlike previous accounts, succeeds in accounting for (i) both their internal structure and the constraints on the embedded NP, and (ii) the relation between their internal structure and any such constraints. First, it is argued that four types of partitive can be distinguished, on the basis of two parameters: (1) the kind of entity denoted by the matrix NP (±set) and (2) the relation between the heads of the matrix and embedded NP (±co-denotational). Using authentic data, the paper subsequently shows that any constraints on the embedded NP apply to only two of these subtypes; it is further argued that these constraints follow directly from the specific properties of these partitives. This, in turn, is taken as evidence that partitives of this kind can be regarded simply as a subtype of the larger group of NPs with the structure N+PP. Finally, it is argued that Functional Discourse Grammar with its different levels and layers of analysis, allows us to capture all the relevant pragmatic, semantic and morphosyntactic properties of the different types of partitives in a systematic and insightful manner.