  Multi-terminal transport setups allow to realize more complex measurements
and functionalities (e.g., transistors) of nanoscale systems than the simple
two-terminal arrangement. Here the steady-state density functional formalism
(i-DFT) for the description of transport through nanoscale junctions with an
arbitrary number of leads is developed. In a three-terminal setup and in the
ideal STM limit where one of the electrodes (the `STM tip') is effectively
decoupled from the junction, the formalism allows to extract its
non-equilibrium spectral function (at arbitrary temperature) while a bias is
applied between the other two electrodes. Multi-terminal i-DFT is shown to be
capable of describing the splitting of the Kondo resonance in an Anderson
impurity in the presence of an applied bias voltage, as predicted by
numerically exact many-body approaches.
