  A non-local model describing the growth of a tree-like transportation network
with given allocation rules is proposed. In this model we focus on tree like
networks, and the network transports the very resource it needs to build
itself. Some general results are given on the viability tree-like networks that
produce an amount of resource based on its amount of leaves while having a
maintenance cost for each node. Some analytical studies and numerical surveys
of the model in "simple" situations are made. The different outcomes are
discussed and possible extensions of the model are then discussed.
