Hierarchical architectures stacking primary, secondary, and tertiary layers are widely employed for the operation and control of islanded dc microgrids (dcmGs) composed of distribution generation units (DGUs), loads, and power lines. However, a comprehensive analysis of all the layers put together is often missing. In this work, we remedy this limitation by setting out a top-to-bottom hierarchical control architecture. Decentralized voltage controllers attached to DGUs form our primary layer. Governed by an MPC-based energy management system (EMS), our tertiary layer generates optimal power references and decision variables for DGUs. In particular, decision variables can turn DGUs on/off and select their operation modes. An intermediary secondary layer translates EMS power references into appropriate voltage signals required by the primary layer. More specifically, to provide a voltage solution, the secondary layer solves an optimization problem embedding power-flow equations shown to be always solvable. Since load voltages are not directly enforced, their uniqueness is necessary for DGUs to produce reference powers handed down by the EMS. To this aim, we deduce a novel uniqueness condition based only on local load parameters. Our control framework, besides being applicable for generic dcmG topologies, can accommodate topological changes caused by EMS commands. Its functioning is validated via simulations on a modified 16-bus dc system.