Power line communications networks (PLCNs) facilitate efficient power management, data access, and monitoring services over a home area network by using a network implementation taking advantage of the built-in power cable infrastructure. A control station with which attached user stations communicate over the power line is used to coordinate the communications process. As serious distortion and losses are incurred by signals that are transmitted across the power line, it is highly desirable to employ relay stations to support the transmission of such data flows. Yet, to date, only limited research results are available for the cross-layer synthesis and management of such a relay-aided power line communications system. In this paper, we develop and study a relay backbone synthesis algorithm (RBSA) that is used to configure the PLC network topology, allowing active source stations to efficiently transport their message flows to the control station. We also present a relay backbone synthesis algorithm under fixed-topology (RBSAF) that enables the system management mechanism to jointly activate selective relay stations and schedule their sharing of the PLC medium, when considering nonadjustable PLC network topologies. Our new computationally efficient RBSA and RBSAF schemes are proven numerically to achieve throughput rates close to the optimal solution.