  The importance of off-shell contributions is discussed for $H\to VV^{(*)}$
with $V\in\{Z,W\}$ for large invariant masses $m_{VV}$ involving a standard
model (SM)-like Higgs boson with $m_H=125$GeV at a linear collider (LC). Both
dominant production processes $e^+e^-\to ZH\to ZVV^{(*)}$ and
$e^+e^-\to\nu\bar\nu H\to\nu\bar\nu VV^{(*)}$ are taken into account, and the
signal processes are compared with background yielding the same final state.
The relative size of the off-shell contributions is strongly dependent on the
centre-of-mass energy. These contributions can have an important impact on the
determination of cross sections and branching ratios. However, the combination
of on- and off-shell contributions can also be utilised to lift degeneracies
allowing to test higher-dimensional operators, unitarity and light and heavy
Higgs interferences in extended Higgs sectors. The latter is demonstrated in
the context of a 2-Higgs-Doublet model. We also discuss the impact of these
aspects for the Large Hadron Collider (LHC) where they are relevant. The
importance of a precise measurement of the Higgs mass for on-shell
contributions in $H\to VV^{(*)}$ is emphasized. A particular focus is put on
methods for extracting the Higgs width at a LC. Off-shell contributions are
shown to have a negligible impact on the width determination at low $\sqrt{s}$
when applying the $Z$ recoil method to extract branching ratios in combination
with an appropriate determination of a partial width. On the other hand,
off-shell contributions can be exploited to constrain the Higgs width in a
similar fashion as in recent analyses at the LHC. It is demonstrated that this
approach, besides relying heavily on theoretical assumptions, is affected by
the negative interference of Higgs and background contributions that may limit
the sensitivity that is achievable with the highest foreseeable statistics at
the LHC and a LC.
