  This article continues the study of diagrams in the bicategory of \'etale
groupoid correspondences. We prove that any such diagram has a groupoid model
and that the groupoid model is a locally compact \'etale groupoid if the
diagram is locally compact and proper. A key tool for this is the relative
Stone-\v{C}ech compactification for spaces over a locally compact Hausdorff
space.
