  A prominent model for transportation networks is branched transport, which
seeks the optimal transportation scheme to move material from a given initial
to a final distribution. The cost of the scheme encodes a higher transport
efficiency the more mass is moved together, which automatically leads to
optimal transportation networks with a hierarchical branching structure. The
two major existing model formulations, either using mass fluxes (vector-valued
measures) or patterns (probabilities on the space of particle paths), are
rather different. Once their equivalence was established, the analysis of
optimal networks could rest on both.
  The transportation cost of classical branched transport is a fractional power
of the transported mass, and several model properties and proof techniques
build on its strict concavity. We generalize the model and its analysis to the
most general class of reasonable transportation costs, essentially increasing,
subadditive functions. This requires several modifications or new approaches.
In particular, for the equivalence between mass flux and pattern formulation it
turns out advantageous to resort to a description via 1-currents, an intuition
which already Xia exploited. In addition, some already existing arguments are
given a more concise and perhaps simpler form. The analysis includes the
well-posedness, a metrization and a length space property of the model cost,
the equivalence between the different model formulations, as well as a few
network properties.
