Nowadays, Internet applications grow significantly in data, the number of users, and geographical distances. Structured data, structured queries, and other features known from traditional database and data integration systems are often mandatory in these new applications. Centralized approaches lack in scalability and distributed systems in the support of these database features. This work focuses on the challenges that occur specifically in the context of query processing in widely distributed systems. We suggest to exploit the advantages of decentralized Peer-to-Peer systems and propose a vertical triple model accompanied by a query algebra and a query engine that make excessive use of modern distributed query processing paradigms. We present an appropriate cost model to enable meaningful query planning and further support guarantees and predictability. An extensive evaluation based on a reference implementation shows the applicability and correctness of the proposed concepts.