In this paper, we examine properties of the tensor powers of quantum mappings Φ. In particular, we review positivity properties of unitary and nonunitary qubit mappings Φ⊗2. For arbitrary finite-dimensional systems, we present the relationship between the positive and completely positive divisibility of dynamical mappings Φ t ⊗ 2 and Φt. A criterion of annihilation of entanglement by an arbitrary qubit mapping Φ⊗2 is found.