In this paper, we propose DBSampler, a query execution mechanism to answer "partial selection" queries in peerto- peer databases. A partial selection query is an arbitrary selection query that is satisfied with a fraction \in of the results; a universal operation with applications in database tuning, query optimization and approximate query processing in peer-to-peer databases. DBSampler is based on an epidemic dissemination algorithm. We model the epidemic dissemination as a percolation problem and by rigorous percolation analysis tune DBSampler per-query and on-thefly to answer partial queries correctly and efficiently. We verify the efficiency of DBSampler in terms of query cost and query time via extensive simulation.