  Massive black hole binaries (MBHBs) represent an unavoidable outcome of
hierarchical galaxy formation, but their dynamical evolution at sub-parsec
scales is poorly understood, due to a combination of uncertainties in
theoretical models and lack of firm observational evidence. In gas rich
environments, it has been shown that a putative extended, steady circumbinary
gaseous disc plays an important role in the MBHB evolution, facilitating its
coalescence. How gas on galactic scales is transported to the nuclear region to
form and maintain such a stable structure is, however, unclear. If, following a
galaxy merger, turbulent gas is condenses in cold clumps and filaments that are
randomly scattered, gas is naturally transported on parsec scales and interacts
with the MBHB in discrete incoherent pockets. The aim of this work is to
investigate the gaseous structures arising from this interaction. We employ a
suite of smoothed-particle-hydrodynamic simulations to study the formation and
evolution of gaseous structures around a MBHB constantly perturbed by the
incoherent infall of molecular clouds. We investigate the influence of the
infall rate and angular momentum distribution of the clouds on the geometry and
stability of the arising structures. We find that the continuous supply of
incoherent clouds is a double-edge sword, resulting in the intermittent
formation and disruption of circumbinary structures. Anisotropic cloud
distributions featuring an excess of co-rotating events generate more prominent
co-rotating circumbinary discs. Similar structures are seen when mostly
counter-rotating clouds are fed to the binary, even though they are more
compact and less stable. In general, our simulations do not show the formation
of extended smooth and stable circumbinary discs, typically assumed in
analytical and numerical investigations of the the long term evolution of
MBHBs. (Abridged)
