We analyze the meanings of university's autonomy throughout western history and capitalism's recent transformations in order to suggest a taxonomy of present universities according to the type of capital enterprise they are imitating. As a first step, we distinguish three dimensions of university's autonomy in the Medieval University and the Enlightenment University models: corporative, reason and financial autonomy. We use them to suggest that current universities are adopting capital enterprises' features in a differentiated way, impacting differently on their autonomy. Thus, we propose a differentiated model called the Differentiated Market-University, integrated by the Single Purpose, the Technological and the Enhanced University. The Single Purpose University acts like a capital enterprise concerning mainly its teaching activity. In the Technological and the Enhanced Universities teaching is also guided by market needs. Nevertheless, they additionally face, differently, the consequences of knowledge's direct contribution to capital's accumulation. The Enhanced University dominates innovation circuits keeping a significant part of its innovation's economic benefit. On the other hand, the Technological University loses those profits. We conclude our article by highlighting the continuities and ruptures between former university models and our taxonomy.