The brains of many organisms are capable of complicated distributed computation underpinned by a highly advanced information processing capacity. Although substantial progress has been made towards characterising the information flow component of this capacity in mature brains, there is a distinct lack of work characterising its emergence during neural development. This lack of progress has been largely driven by the lack of effective estimators of information processing operations for the spiking data available for developing neural networks. Here, we leverage recent advances in this estimation task in order to quantify the changes in information flow during development. We do so by studying the changes in the intrinsic dynamics of the spontaneous activity of developing dissociated neural cell cultures. We find that the quantity of information flowing across these networks undergoes a dramatic increase across development. Moreover, the spatial structure of these flows is locked-in during early development, after which there is a substantial temporal correlation in the information flows across recording days. We analyse the flow of information during the crucial periods of population bursts. We find that, during these bursts, nodes undertake specialised computational roles as either transmitters, mediators or receivers of information, with these roles tending to align with their spike ordering — either early, mid or late in the bursts. Further, we find that the specialised computational roles occupied by nodes during bursts tend to be locked-in early. Finally, we briefly compare these results to information flows in a model network developing according to an STDP learning rule from a state of independent firing to synchronous bursting. The phenomena of large increases in information flow, early lock-in of information flow spatial structure and computational roles based on burst position were also observed in this model, hinting at the broader generality of these phenomena. AUTHOR SUMMARY This paper studies the development of computation in biological systems by analysing changes in the flow of information in developing neural cell cultures. Although there have been a number of previous studies of information flows in neural cell cultures, this work represents the first study which compares information flows in the intrinsic dynamics across development time. Moreover, we make use of a recently proposed continuous-time transfer entropy estimator for spike trains, which, in comparison to the discrete-time estimator used previously, is able to capture important effects occurring on both small and large timescales simultaneously. We find that information flows begin to emerge after 5-10 days of activity, and crucially, the spatial structure of information flows remains significantly temporally correlated over the first month of recording. Furthermore, the magnitude of information flows across the culture are strongly related to burst position, and the roles of regions as information flow sources, sinks and mediators are found to remain consistent across development. Finally, we confirm that these early lock-ins also occur in a simple model network developing under an STDP update rule, suggesting a plausible mechanism undergirding this phenomenon.