The essential skeleton is an invariant of a degeneration that appears in both Berkovich geometry and minimal model theory. I will show that for degenerations with a semistable model, the essential skeleton of a product of degenerations is the product of their skeleta. As an application, we are able to describe the homeomorphism type of some degenerations of hyperkähler varieties, both for a Hilbert scheme of degenerating K3 surfaces and for a Kummer variety associated to a degeneration of an abelian surface. This is joint work with Enrica Mazzon.