  We analyze tight informationally complete measurements for arbitrarily large
multipartite systems and study their configurations of entanglement. We
demonstrate that tight measurements cannot be exclusively composed neither of
fully separable nor maximally entangled states. We establish an upper bound on
the maximal number of fully separable states allowed by tight measurements and
investigate the distinguished case, in which every measurement operator carries
the same amount of entanglement. Furthermore, we introduce the notion of nested
tight measurements, i.e. multipartite tight informationally complete
measurements such that every reduction to a certain number of parties induces a
lower dimensional tight measurement, proving that they exist for any number of
parties and internal levels.
