  We investigate qualitative properties of the underlying scheme of
Rapoport-Zink formal moduli spaces of p-divisible groups, resp. Shtukas. We
single out those cases when the dimension of this underlying scheme is zero,
resp. those where the dimension is maximal possible. The model case for the
first alternative is the Lubin-Tate moduli space, and the model case for the
second alternative is the Drinfeld moduli space. We exhibit a complete list in
both cases.
