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Massive black hole binaries (MBHBs) represent an unavoidable outcome ofhierarchical galaxy formation, but their dynamical evolution at sub-parsecscales is poorly understood, due to a combination of uncertainties intheoretical models and lack of firm observational evidence. In gas richenvironments, it has been shown that a putative extended, steady circumbinarygaseous disc plays an important role in the MBHB evolution, facilitating itscoalescence. How gas on galactic scales is transported to the nuclear region toform and maintain such a stable structure is, however, unclear. If, following agalaxy merger, turbulent gas is condenses in cold clumps and filaments that arerandomly scattered, gas is naturally transported on parsec scales and interactswith the MBHB in discrete incoherent pockets. The aim of this work is toinvestigate the gaseous structures arising from this interaction. We employ asuite of smoothed-particle-hydrodynamic simulations to study the formation andevolution of gaseous structures around a MBHB constantly perturbed by theincoherent infall of molecular clouds. We investigate the influence of theinfall rate and angular momentum distribution of the clouds on the geometry andstability of the arising structures. We find that the continuous supply ofincoherent clouds is a double-edge sword, resulting in the intermittentformation and disruption of circumbinary structures. Anisotropic clouddistributions featuring an excess of co-rotating events generate more prominentco-rotating circumbinary discs. Similar structures are seen when mostlycounter-rotating clouds are fed to the binary, even though they are morecompact and less stable. In general, our simulations do not show the formationof extended smooth and stable circumbinary discs, typically assumed inanalytical and numerical investigations of the the long term evolution ofMBHBs. (Abridged)

Accretion of clumpy cold gas onto massive black holes binaries: the challenging formation of extended circumbinary structures