  Let $K$ be a $p$-adic field. We continue to develop the theory of rigid
analytic $p$-divisible groups over $K$. For example, we explain how to find
back the category of Banach-Colmez spaces from rigid analytic $p$-divisible
groups "in finite level" without perfectoid spaces. We then establish some
results about families of rigid analytic $p$-divisible groups. This allows us
to prove a "minimality" result in the sense of birationnal geometry for
integral models of unramified Rapoport-Zink spaces.
