Contemporary state-of-the-art runtime systems underlying widely utilized general purpose parallel programming languages and libraries like OpenMP, MPI, or OpenCL provide the foundation for accessing the parallel capabilities of modern computing architectures. In the tradition of their respective imperative host languages those runtime systems' main focus is on providing means for the distribution and synchronization of operations --- while the organization and management of manipulated data is left to application developers. Consequently, the distribution of data remains inaccessible to those runtime systems. However, many desirable system-level features depend on a runtime system's ability to exercise control on the distribution of data. Thus, program models underlying traditional systems lack the potential for the support of those features. In this paper, we present a novel application model granting parallel runtime systems system-wide control over the distribution of user-defined shared data structures. Our model utilizes the high-level nature of parallel programming languages, in particular, the usage of well-typed data structures and the associated hiding of implementation details from the application developers. By being based on a generalization of such data structures and extending the resulting abstraction with features facilitating the automated management of the distribution of those, our model enables runtime systems to dynamically influence the placement and replication of shared data. This paper covers a rigorous formal description of our application model, as well as details on our prototype implementation and experimental results demonstrating its ability to efficiently and scalably manage various data structures in real-world environments.