  We give a detailed account of the Hamiltonian GNH analysis of the
parametrized unimodular extension of the Holst action. The purpose of the paper
is to derive, through the clear geometric picture furnished by the GNH method,
a simple Hamiltonian formulation for this model and explain why it is difficult
to arrive at it in other approaches. We will also show how to take advantage of
the field equations to anticipate the simple form of the constraints that we
find in the paper.
