Macroscopic brain organisation emerges early in life, even prenatally, and continues to develop through adolescence and into early adulthood. The emergence and continual refinement of large-scale brain networks, connecting neuronal populations across anatomical distance, allows for increasing functional integration and specialisation. This process is thought crucial for the emergence of complex cognitive processes. But how and why is this process so diverse? We used structural neuroimaging collected from a large diverse cohort, to explore how different features of macroscopic brain organisation are associated with diverse cognitive trajectories. We used diffusion-weighted imaging (DWI) to construct whole-brain white-matter connectomes. A simulated attack on each child's connectome revealed that some brain networks were strongly organized around highly connected 'hubs'. The more children's brains were critically dependent on hubs, the better their cognitive skills. Conversely, having poorly integrated hubs was a very strong risk factor for cognitive and learning difficulties across the sample. We subsequently developed a computational framework, using generative network modelling (GNM), to model the emergence of this kind of connectome organisation. Relatively subtle changes within the wiring rules of this computational framework give rise to differential developmental trajectories, because of small biases in the preferential wiring properties of different nodes within the network. Finally, we were able to use this GNM to implicate the molecular and cellular processes that govern these different growth patterns.