"Semi-discrete optimal transport between a discrete source and a continuous target has intriguing geometric properties and applications in modelling and numerical methods. Unbalanced transport, which allows the comparison of measures with unequal mass, has recently been studied in great detail by various authors. In this talk we consider the combination of both concepts. The tessellation structure of semi-discrete transport survives and there is an interplay between the length scales of the discrete source and unbalanced transport which leads to qualitatively new regimes in the crystallization limit."