This paper investigates case assignment in prepositional phrases in Ancient Greek and presents evidence that it is determined by the function of the PP and not by the preposition. It is shown that most of the prepositional lexical items involve a root and a formative with prepositional categorizing function, providing evidence for a decomposition approach which suggests that the prepositional lexical item is a morphosyntactic formation that lexicalizes a functional structure which is responsible for its semantic and syntactic properties, including case assignment. This functional structure contains, among others, a categorizing p head, relevant to the lexicalization of the structure by means of a preposition, and a pCASE head, which is responsible for the case assigning properties of the structure. It is also argued that these two heads are distinct from each other as suggested by the way prepositions behave in terms of case assignment in prepositional prefixation constructions.