We propose several localized sensor area coverage protocols, for arbitrary ratio of sensing and transmission radii. Sensors are assumed to be time synchronized, and active sensors are determined at the beginning of each round. The approach has a very small communication overhead since prior knowledge about neighbor existence is not required. Each node selects a random timeout and listens to messages sent by other nodes before the timeout expires. Sensor nodes whose sensing area is not fully covered (or fully covered but with a disconnected set of active sensors) when the deadline expires decide to remain active for the considered round, and transmit a message announcing their activity status. There are four variants in our approach, depending on whether or not negative and retreat messages are transmitted. Covered nodes decide to sleep, with or without transmitting a negative acknowledgment to inform neighbors about the status. After hearing from more neighbors, active sensors may obs...