  Motivated by establishing holographic renormalization for gravitational
theories with non-metricity and torsion, we present a new and efficient general
method for calculating Gibbons-Hawking-York (GHY) terms. Our method consists of
linearizing any nonlinearity in curvature, torsion or non-metricity by
introducing suitable Lagrange multipliers. Moreover, we use a split formalism
for differential forms, writing them in $(n-1)+1$ dimensions. The boundary
terms of the action are manifest in this formalism by means of Stokes' theorem,
such that the compensating GHY term for the Dirichlet problem may be read off
directly. We observe that only those terms in the Lagrangian that contain
curvature contribute to the GHY term. Terms polynomial solely in torsion and
non-metricity do not require any GHY term compensation for the variational
problem to be well-defined. We test our method by confirming existing results
for Einstein-Hilbert and four-dimensional Chern-Simons modified gravity.
Moreover, we obtain new results for Lovelock-Chern-Simons and metric-affine
gravity. For all four examples, our new method and results contribute to a new
approach towards a systematic hydrodynamic expansion for spin and hypermomentum
currents within AdS/CFT.
