Mobile UNITY refers to a notation system and proof logic initially designed to accommodate the special needs of the emerging field of mobile computing. The model allows one to define units of computation and mobility and the formal rules for coordination among them in a highly decoupled manner. In this paper, we reexamine the expressive power of the Mobile UNITY coordination constructs from a new perspective rooted in the notion that disciplined usage of a powerful formal model must rely on formally defined schemas. Several coordination schemas are introduced and formalized. They examine the relationship between Mobile UNITY and other computing models and illustrate the mechanics of employing Mobile UNITY as the basis for a formal semantic characterization of coordination models.