  We introduce a decentralized replication strategy for peer-to-peer file
exchange based on exhaustive exploration of the neighborhood of any node in the
network. The replication scheme lets the replicas evenly populate the network
mesh, while regulating the total number of replicas at the same time. This is
achieved by self adaptation to entering or leaving of nodes. Exhaustive
exploration is achieved by a spiral walk algorithm that generates a number of
messages linearly proportional to the number of visited nodes. It requires a
dedicated topology (a triangular mesh on a closed surface). We introduce
protocols for node connection and departure that maintain the triangular mesh
at low computational and bandwidth cost. Search efficiency is increased using a
mechanism based on dynamically allocated super peers. We conclude with a
discussion on experimental validation results.
