Let denote the set of all holomorphic functions in the open unit disk and let be a holomorphic selfmap of . Suppose that and are two function spaces defined on . The map is said to have the -to- pullback property if for every . Let be an arc on the unit circle and , the associated Carleson box. In the present paper, the author studies the -to- pullback property for
and for and . A complete characterization of the bounded and compact composition operators on the weighted Bloch space is given. Unfortunately, this paper has many grammatical errors and the title of reference  is not correct.