The observation that not all grammatical realizations in heritage languages can be attributed to transfer from a dominant language has been emphasized in several recent works. This paper provides further arguments in this direction from heritage Romanian. As opposed to standard Romanian, the heritage Romanian data examined here do not exhibit a restriction which blocks overt definiteness on a differentially marked object (DOM), when the latter is unmodified but interpreted as definite. Moreover, in heritage Romanian there appear to be differences between the differential marker and (other) prepositions when it comes to interactions with overt definiteness. It is shown that the preservation of overt definiteness cannot be reduced to transfer; some of the dominant languages at stake, namely Serbian and Russian are determinerless, with nominals being used bare regardless of their syntactic function. The heritage data in turn give support to a theory under which the differential marker must be structurally set aside from (other) prepositions. If the latter spell out a P projection, the differential marker is the spell out of complex internal structure of certain classes of objects, which must project at least a DP. This structural complexity for DOM is transparent in other Romance languages, where definiteness is equally obligatory on the surface, if a definite interpretation is intended. Thus, the DOM-overt definiteness setting in the heritage data follows from predictable paths of language variation.