  For a minimal affinization over a quantum loop algebra of type BC, we provide
a character formula in terms of Demazure operators and multiplicities in terms
of crystal bases. We also provide a simple formula for the limit of characters.
These are achieved by verifying that its graded limit (a variant of a classical
limit) is isomorphic to some multiple generalization of a Demazure module, and
by determining the defining relations of the graded limit.
