Summary: Personalized PageRank expresses link-based page quality around userselected pages in a similar way as PageRank expresses quality over the entire web. Existing personalized PageRank algorithms can, however, serve online queries only for a restricted choice of pages. In this paper we achieve full personalization by a novel algorithm that precomputes a compact database; using this database, it can serve online responses to arbitrary user-selected personalization. The algorithm uses simulated random walks; we prove that for a fixed error probability the size of our database is linear in the number of web pages. We justify our estimation approach by asymptotic worst-case lower bounds: we show that on some sets of graphs, exact personalized PageRank values can only be obtained from a database of size quadratic in the number of vertices. Furthermore, we evaluate the precision of approximation experimentally on the Stanford WebBase graph.