In recent years, specific cortical networks have been proposed to be crucial for sustaining consciousness, including the posterior hot zone and frontoparietal resting state networks (RSN). Here, we computationally evaluate the relative contributions of three RSNs - the default mode network (DMN), the salience network (SAL), and the central executive network (CEN) - to consciousness and its loss during propofol anaesthesia. Specifically, we use dynamic causal modelling (DCM) of 10 min of high-density EEG recordings (N = 10, 4 males) obtained during behavioural responsiveness, unconsciousness and post-anaesthetic recovery to characterise differences in effective connectivity within frontal areas, the posterior 'hot zone', frontoparietal connections, and between-RSN connections. We estimate - for the first time - a large DCM model (LAR) of resting EEG, combining the three RSNs into a rich club of interconnectivity. Consistent with the hot zone theory, our findings demonstrate reductions in inter-RSN connectivity in the parietal cortex. Within the DMN itself, the strongest reductions are in feed-forward frontoparietal and parietal connections at the precuneus node. Within the SAL and CEN, loss of consciousness generates small increases in bidirectional connectivity. Using novel DCM leave-one-out cross-validation, we show that the most consistent out-of-sample predictions of the state of consciousness come from a key set of frontoparietal connections. This finding also generalises to unseen data collected during post-anaesthetic recovery. Our findings provide new, computational evidence for the importance of the posterior hot zone in explaining the loss of consciousness, highlighting also the distinct role of frontoparietal connectivity in underpinning conscious responsiveness, and consequently, suggest a dissociation between the mechanisms most prominently associated with explaining the contrast between conscious awareness and unconsciousness, and those maintaining consciousness.