  We present a detailed analysis of gravity in a partial Bondi gauge, where
only the three conditions $g_{rr}=0=g_{rA}$ are fixed. We relax in particular
the so-called determinant condition on the transverse metric, which is only
assumed to admit a polyhomogeneous radial expansion. This is sufficient in
order to build the solution space, which here includes a cosmological constant,
time-dependent sources in the boundary metric, logarithmic branches, and an
extra trace mode at subleading order in the transverse metric. The evolution
equations are studied using the Newman-Penrose formalism in terms of covariant
functionals identified from the Weyl scalars, and we build the explicit
dictionary between this formalism and the tensorial Einstein equations. This
provides in particular a new derivation of the (A)dS mass loss formula. We then
study the holographic renormalisation of the symplectic potential, and the
transformation laws under residual asymptotic symmetries. The advantage of the
partial Bondi gauge is that it allows to contrast and treat in a unified manner
the Bondi-Sachs and Newman-Unti gauges, which can each be reached upon imposing
a further specific gauge condition. The differential determinant condition
leads to the $\Lambda$-BMSW gauge, while a differential condition on $g_{ur}$
leads to a generalized Newman-Unti gauge. This latter gives access to a new
asymptotic symmetry which acts on the asymptotic shear and further extends the
$\Lambda$-BMSW group by an extra abelian radial translation. This generalizes
results which we have recently obtained in three dimensions.
