Current models for melt segregation and ascent are not adequate to accurately describe transport and accumulation in combination. We propose that transport is discontinuous and in batches, and that accumulation occurs by stepwise merging of batches. A simple numerical model of jostling spheres that merge when they touch was used to represent stepwise accumulation and transport of batches by propagation of hydrofractures. Results of the numerical model indicate that such a system may quickly develop into a self-organised critical (SOC) state. In this state, the distribution of melt batch volumes can be described by a power law, with an exponent m that lies between 2/3 and 1. Once a self-organised critical state is established, the system is capable of discharging any additional melt without further change to itself. Deformation aids melt extraction efficiency, as it increases the mobility of hydrofractures, enhances accumulation and hence lowers the exponent m. Full connectivity of melt needs never to be reached in the system and melt transport and extraction can occur at very low melt fractions. The chemical evolution of melt from source to emplacement level will be governed by the discontinuous mixing and mingling of batches, each with different histories, and possibly different sources. If no subsequent homogenisation occurs in a magma chamber or the final emplacement structure, the process can be identified by chemical heterogeneity of plutons and volcanic rocks.