  Given a finite dimensional pure state transformation restricted by
entanglement assisted local operations and classical communication (ELOCC), we
derive minimum and maximum bounds on the entanglement of an ancillary catalyst
that allows that transformation. These bounds are non-trivial even when the
Schmidt number of both the original and ancillary states becomes large. We
identify a lower bound for the dimension of a catalyst allowing a particular
ELOCC transformation. Along with these bounds, we present further constraints
on ELOCC transformations by identifying restrictions on the Schmidt
coefficients of the target state. In addition, an example showing the existence
of qubit ELOCC transformations with multiple ranges of potential ancillary
states is provided. This example reveals some additional difficulty in finding
strict bounds on ELOCC transformations, even in the qubit case. Finally, a
comparison of the bounds in this paper with previously discovered bounds is
presented.
