  We examine the powers of entanglement-assisted transformation and
multiple-copy entanglement transformation. First, we find a sufficient
condition of when a given catalyst is useful in producing another specific
target state. As an application of this condition, for any non-maximally
entangled bipartite pure state and any integer $n$ not less than 4, we are able
to explicitly construct a set of $n\times n$ quantum states which can be
produced by using the given state as a catalyst. Second, we prove that for any
positive integer $k$, entanglement-assisted transformation with $k\times
k$-dimensional catalysts is useful in producing a target state if and only if
multiple-copy entanglement transformation with $k$ copies of state is useful in
producing the same target. Moreover, a necessary and sufficient condition for
both of them is obtained in terms of the Schmidt coefficients of the target.
This equivalence of entanglement-assisted transformation and multiple-copy
entanglement transformation implies many interesting properties of entanglement
transformation. Furthermore, these results are generalized to the case of
probabilistic entanglement transformations.
