We present SPARSI, a theoretical framework for partitioning sensitive data across multiple non-colluding adversaries. Most work in privacy-aware data sharing has considered disclosing summaries where the aggregate information about the data is preserved, but sensitive user information is protected. Nonetheless, there are applications, including online advertising, cloud computing and crowdsourcing markets, where detailed and fine-grained user-data must be disclosed. We consider a new data sharing paradigm and introduce the problem of privacy-aware data partitioning, where a sensitive dataset must be partitioned among k untrusted parties (adversaries). The goal is to maximize the utility derived by partitioning and distributing the dataset, while minimizing the amount of sensitive information disclosed. The data should be distributed so that an adversary, without colluding with other adversaries, cannot draw additional inferences about the private information, by linking together multiple pieces of information released to her. The assumption of no collusion is both reasonable and necessary in the above application domains that require release of private user information. SPARSI enables us to formally define privacy-aware data partitioning using the notion of sensitive properties for modeling private information and a hypergraph representation for describing the interdependencies between data entries and private information. We show that solving privacy-aware partitioning is, in general, NP-hard, but for specific information disclosure functions, good approximate solutions can be found using relaxation techniques. Finally, we present a local search algorithm applicable to generic information disclosure functions. We apply SPARSI together with the proposed algorithms on data from a real advertising scenario and show that we can partition data with no disclosure to any single advertiser.