Boundary Components of Mumford-Tate Domains

We study certain spaces of nilpotent orbits in Hodge domains, and treat a number of examples. More precisely, we compute the Mumford-Tate group of the limit mixed Hodge structure of a generic such orbit. The result is used to present these spaces as iteratively fibered algebraic-group orbits in a minimal way. We conclude with two applications to variations of Hodge structure.