A scalable blind source separation paradigm aimed at sensor networks is described. The approach facilitates an unlimited number of sensors and sources and does not require a fusion centre. It is based on a so-called ownership principle, where each network node aims to extract (own) a source signal that is not already extracted (owned) by another network node. Nodes that own a source signal broadcast that signal to user nodes outside the network. Nodes that do not currently own a source signal do not transmit information and can be active intermittently. A natural application of the method is a distributed microphone network in a multi-talker environment, with as user nodes hearing aids or telephone interface devices. Such a network can stretch across buildings or neighbourhoods. Simulations using independent component analysis (ICA) indicate the validity of the principles of the method.