The contemporary university has its place amid a world in total motion. The issue arises, then, as to what it is it to try to shape a university in the context of a world that lacks stability. The thesis argued here is twofold: (1) that the university should take seriously its entwinement with the world; indeed, with large eco-systems of the world; (2) that the instrumentality that is so prevalent in universities should be displaced by an ethic of collective care for the world. The logic of this double-thesis is plotted by examining the three matters of transdisciplinarity, leadership and quality. The article concludes by reflecting that university 'design' is a misnomer. Rather, universities can only be conjectured, imagined and ventured forth and with some delicacy.