  We first investigate a connected quiver consisting of all dominant maximal
weights for an integrable highest weight module in affine type C. This quiver
provides an efficient method to obtain all dominant maximal weights. Then, we
completely determine the representation type of cyclotomic
Khovanov-Lauda-Rouquier algebras of arbitrary level in affine type C, by using
the quiver we construct. We also determine the Morita equivalence classes and
graded decomposition matrices of certain representation-finite and tame
cyclotomic KLR algebras.
