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The normal myelination of neuronal axons is essential to neurodevelopment, allowing fast inter-neuronal communication. The most dynamic period of myelination occurs in the first few years of life, in concert with a dramatic increase in cognitive abilities. How these processes relate, however, is still unclear. Here we aimed to use a data-driven technique to parcellate developing white matter into regions with consistent white matter growth trajectories and investigate how these regions related to cognitive development. In a large sample of 183 children aged 3 months to 4 years, we calculated whole brain myelin volume fraction (VFM ) maps using quantitative multicomponent relaxometry. We used spatial independent component analysis (ICA) to blindly segment these quantitative VFM images into anatomically meaningful parcels with distinct developmental trajectories. We further investigated the relationship of these trajectories with standardized cognitive scores in the same children. The resulting components represented a mix of unilateral and bilateral white matter regions (e.g., cortico-spinal tract, genu and splenium of the corpus callosum, white matter underlying the inferior frontal gyrus) as well as structured noise (misregistration, image artifact). The trajectories of these regions were associated with individual differences in cognitive abilities. Specifically, components in white matter underlying frontal and temporal cortices showed significant relationships to expressive and receptive language abilities. Many of these relationships had a significant interaction with age, with VFM becoming more strongly associated with language skills with age. These data provide evidence for a changing coupling between developing myelin and cognitive development.