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Australia established a demand-driven funding model for government-subsidised undergraduate places at public universities between 2012 and 2017. This allowed public universities to expand subsidised undergraduate places over this period. However, private universities and colleges did not have access to demand-driven funding but nonetheless grew domestic student enrolments by 38% over the same period, an unexpected difference given that demand-driven funding allowed public universities to expand enrolments with few limitations. To explain differences in growth by institution type, a supply and demand model relevant to public universities and private universities and colleges is developed. The model is used to understand enrolment dynamics and how providers responded to the demand-driven funding environment. Drawing on novel higher education statistics, four hypotheses for the unexpected enrolment growth in private universities and colleges are tested: reputational factors; disciplinary specialisation; price; and appeal to disadvantaged student groups. The data reveal some support for each hypothesis but show disciplinary specialisation is the strongest explanation of enrolment growth outside public universities. The findings illustrate how less established private institutions can grow and compete with more established public universities by responding to market demand and offering specialised programmes to meet that demand. [ABSTRACT FROM AUTHOR]