A key feature of the fetal period is the rapid emergence of organised patterns of spontaneous brain activity. However, characterising this process in utero using functional MRI is inherently challenging and requires analytical methods which can capture the constituent developmental transformations. Here, we introduce a novel analytical framework, termed "maturational networks" (matnets), that achieves this by modelling functional networks as an emerging property of the developing brain. Compared to standard network analysis methods that assume consistent patterns of connectivity across development, our method incorporates age-related changes in connectivity directly into network estimation. We test its performance in a large neonatal sample, finding that the matnets approach characterises adult-like features of functional network architecture with a greater specificity than a standard group-ICA approach; for example, our approach is able to identify a nearly complete default mode network. In the in-utero brain, matnets enables us to reveal the richness of emerging functional connections and the hierarchy of their maturational relationships with remarkable anatomical specificity. We show that the associative areas play a central role within prenatal functional architecture, therefore indicating that functional connections of high-level associative areas start emerging prior to exposure to the extra-utero environment.