  Topologically protected qubits based on nanostructures hosting Majorana bound
states (MBSs) hold great promise for fault-tolerant quantum computing. We study
the transport properties of nanowire networks hosting MBSs with a focus on the
effects of the charging energy and the overlap between neighboring MBSs in
short mesoscopic samples. In particular, we investigate structures hosting four
MBSs such as T-junctions and Majorana boxes. Using a master equation in the
Markovian approximation, we discuss the leading transport processes mediated by
the MBSs. Single-electron tunneling and processes involving creation and
annihilation of Cooper pairs dominate in the sequential tunneling limit. In the
cotunneling regime the charge in the MBSs network is fixed and transport is
governed by transitions via virtual intermediate states. Our results show that
four-terminal measurements in the T-junction and Majorana box geometries can be
useful tools for the characterization of the properties of MBSs with finite
overlaps and charging energy.
