The function of the plant’s vasculature, incorporating both phloem and xylem, is of fundamental importance to the survival of all higher plants. Although the physiological mechanism involved in these two transport pathways has been known for some time, quantitative modelling of this has been slow to develop. 1-D continuous models have shown that the proposed mechanisms are quantitatively plausible (Thompson and Holbrook 2003) but more complex geometries (architectures) have remained out of reach because of mathematical difficulties. In this work, we extend the alternative modular approach by Daudet et al. (2002) using recently developed numerical tools which allow us to model complex architectures. After a full description of the extended model, we first show that it efficiently reproduces the results of the continuous approach when applied to the same simple configurations. The model is then applied to a more complex configuration with two sinks, confirming that sink priority is an emergent property of the Münch flow as earlier found with a minimalist model (Minchin et al. 1993). It is further shown how source leaf transpiration can change the relative carbon allocation rates among sinks.