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We propose a novel distributed randomized algorithm for self-deployment of a network of mobile robotic sensors in the problem of blanket coverage. The aim is to deploy sensors in a bounded connected region so that any point of the region is sensed by at least one mobile robotic sensor. The proposed algorithm is based only on information about the closest neighbours of each sensor. The monitoring region is of an arbitrary shape and not known to the sensors a priori. We give mathematically rigorous proofs of asymptotic optimality and convergence with probability 1 of the proposed algorithm.