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Data generation increases at highly dynamic rates, making its storage, processing, and update costs at one central location excessive. The P2P paradigm emerges as a powerful model for organizing and searching large data repositories distributed over independent sources. Advanced query operators, such as skyline queries, are necessary in order to help users handle the huge amount of available data. A skyline query retrieves the set of nondominated data points in a multidimensional data set. Skyline query processing in P2P networks poses inherent challenges and demands nontraditional techniques, due to the distribution of content and the lack of global knowledge. Relying on a superpeer architecture, we propose a threshold-based algorithm, called SKYPEER and its variants, for efficient computation of skyline points in arbitrary subspaces, while reducing both computational time and volume of transmitted data. Furthermore, we address the problem of routing skyline queries over the superpeer network and we propose an efficient routing mechanism, namely SKYPEER+, which further improves the performance by reducing the number of contacted superpeers. Finally, we provide an extensive experimental evaluation showing that our approach performs efficiently and provides a viable solution when a large degree of distribution is required.