A system for forming and maintaining one or more networks of devices connected to a shared includes processes for: (a) forming a logical network on the shared media; (b) discovering devices connected to the shared medium; (c) assigning (or acquiring) devices to a logical network; and (d) maintaining a logical network. The system also defines a message format and protocol for communication over the shared media. The protocol uses a two-level address scheme (e.g., a logical network ID and a device ID) and defines several message types used to support the above processes and other useful features. A logical network includes an address space arbiter (ASA) and, typically, one or more devices attached to the shared media. An acquisition authority (AA), interacting with the ASA, is required to complete acquisition of a device by a logical network.