  In this paper we redefine the well-known metric-affine Hilbert Lagrangian in
terms of a spin-connection and a spin-tetrad. On applying the Poincar\'e-Cartan
method and using the geometry of gauge-natural bundles, a global gravitational
superpotential is derived. On specializing to the case of the Kosmann lift, we
recover the result originally found by Kijowski (1978) for the metric (natural)
Hilbert Lagrangian. On choosing a different, suitable lift, we can also recover
the Nester-Witten 2-form, which plays an important role in the energy
positivity proof and in many quasi-local definitions of mass.
