  We point out that there exists a family of transformations acting on BF-type
Lagrangians of gravity, with Lagrangians related by such a transformation
corresponding to classically equivalent theories. A transformation of this type
corresponds to a particular field redefinition. We discuss both the chiral and
non-chiral cases. In the chiral case there is a one-parameter, and in the
non-chiral case a two-parameter family of such transformations. In the chiral
setup, we use these transformations to give an alternative derivation of the
chiral BF plus potential formulation of General Relativity that was proposed
recently. In the non-chiral case, we show that there is a new BF plus potential
type formulation of GR. We also make some remarks on the non-chiral pure
connection formulation.
