The Overset (Chimera) Grid approach has many practical benefits for unsteady moving grid simulations. However, an inherent requirement and challenge is the need to establish the inter-grid communication and donor-receiver pairs where the solution must be exchanged between overlapping grids via a process formally known as overset grid assembly. Furthermore, in the context of large-scale unsteady simulations, grid assembly is performed at each time-step and typically must operate on a set of already distributed grids. We call this problem the distributed overset grid assembly problem. The implementation of techniques to efficiently handle the distributed overset grid assembly problem is the primary topic of this paper. In particular, this paper makes the following technical contributions. First, we formulate the distributed overset grid assembly problem and present its challenges. Second, we present techniques that can handle both 2-D and 3-D, structured, unstructured, or mixed element, distributed, overset grids. Finally, we present preliminary performance results using a Wing-Store Separation configuration.