One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product. In this paper we continue the work of  to adapt the machinery of globular operads  to this task. The resulting theory includes the Gray tensor product of 2-categories and the Crans tensor product  of Gray categories. Moreover much of the previous work on the globular approach to higher category theory is simplified by our new foundations, and we illustrate this by giving an expedited account of many aspects of Cheng's analysis  of Trimble's definition of weak n-category. By way of application we obtain an "Ekmann-Hilton" result for braided monoidal 2-categories, and give the construction of a tensor product of A-infinity algebras.