On the existence and uniqueness of type II Hermite–Padé polynomials

New concepts are introduced in the work. They are quite normal index and a quite perfect system of functions. Using these concepts, a uniqueness criterion was formulated and proved, explicit determinant representations of type II Hermite–Padé polynomials for an arbitrary system of power series were obtained. The results obtained complement and generalize the well-known result in the theory of Hermite–Padé approximations.