Grain growth during the solidification of an alloy is accompanied by the enrichment of the surrounding liquid phase in chemical species. The resulting diffusion fields induce interactions between the grains that are strongly dependent on their spatial arrangement. The influence of these diffusive interactions is not limited to the shapes and sizes of grains but also controls the overall kinetics of the transformation. In this study we investigate the role of the spatial arrangement of equiaxed grains in the average growth kinetics of an ensemble of grains. We perform full-field simulations of different grain ensembles using the mesoscopic grain envelope model (GEM). We show that the growth kinetics of randomly arranged ensembles is fundamentally different from that of periodic arrangements. We provide an explanation of this difference through analyses of the behaviour of individual grains in their local neighbourhood, defined by a Voronoi tessellation. Finally, we compare the full-field GEM simulations to stateof-the-art mean-field models and we point out the limitations of the latter in the prediction of dendritic growth.