Most current models of assimilate carbohydrate partitioning are based on growth patterns observed under a range of experimental conditions, from which a set of empirical rules are derived to simulate partitioning. As a result, they are not good at extrapolating to other conditions; this requires a mechanistic approach, which only transport-resistance (TR) models currently provide. We examine an approach to incorporating recent progress in phloem physiology into the TR approach, which leads to a ‘minimalist’ Münch model of a branched system with competing sinks. In vivo whole-plant measurements have demonstrated that C-flow rates are dependent not only on the properties of the sink, but also on the properties of the whole transport system, and the detailed dynamics of this behaviour is mimicked by the proposed model. This model provides a sound theoretical framework for an unambiguous definition of sink and source strengths, with sink priority being an emergent property of the model. Further developments are proposed, some of which have already had limited application, to cope with the complexity of plants; the emphasis is on a modular approach, together with the importance of choosing the appropriate scale level for both structure and function. Whole-plant experiments with in vivo measurement of the phloem dynamics will be needed to help with this choice.