Too few studies of elite private schools consider how they derive power and prestige from their relationships and interactions with other social and political groups and institutions, including the State. This paper contributes to elite school studies by examining the relationality between the Australian State and private sector schools around how government funds public and private education. Of all Australian students, 35.5% attend private schools. All private schools, including elite schools, receive significant amounts of taxpayers' money. After explaining the complex policy architecture of this funding regime, this paper offers a fresh set of conceptual resources to help deepen the analysis of this situation. We argue that the whole Australian private school sector operates as an accumulation economy, essentially utilising public sector resources to enlarge, enrich and sustain itself. This happens via three dynamics -- accumulation by extraction, by mystification and by depletion. We show how elite schools are part of, and benefit from, each.