  We report off-shell Noether currents obtained from off-shell Noether
potentials for first-order general relativity described by $n$-dimensional
Palatini and Holst Lagrangians including the cosmological constant. These
off-shell currents and potentials are achieved by using the corresponding
Lagrangian and the off-shell Noether identities satisfied by diffeomorphisms
generated by arbitrary vector fields, local $SO(n)$ or $SO(n-1,1)$
transformations, `improved diffeomorphisms', and the `generalization of local
translations' of the orthonormal frame and the connection. A remarkable aspect
of our approach is that we do {\it not} use Noether's theorem in its direct
form. By construction, the currents are off-shell conserved and lead naturally
to the definition of off-shell Noether charges. We also study what we call the
`half off-shell' case for both Palatini and Holst Lagrangians. In particular,
we find that the resulting diffeomorphism and local $SO(3,1)$ or $SO(4)$
off-shell Noether currents and potentials for the Holst Lagrangian generically
depend on the Immirzi parameter, which holds even in the `half off-shell' and
on-shell cases. We also study Killing vector fields in the `half off-shell' and
on-shell cases. The current theoretical framework is illustrated for the `half
off-shell' case in static spherically symmetric and
Friedmann--Lemaitre--Robertson--Walker spacetimes in four dimensions.
