  The processes driving gas accretion on to supermassive black holes (SMBHs)
are still poorly understood. Angular momentum conservation prevents gas within
$\sim10\,$pc of the black hole from reaching radii $\sim10^{-3}\,$pc where
viscous accretion becomes efficient. Here we present simulations of the
collapse of a clumpy shell of swept-up isothermal gas, which is assumed to have
formed as a result of feedback from a previous episode of AGN activity. The gas
falls towards the SMBH forming clumps and streams, which intersect, collide,
and often form a disc. These collisions promote partial cancellations of
angular momenta, resulting in further infall and more collisions. This
continued collisional cascade generates a tail of gas with sufficiently small
angular momenta and provides a viable route for gas inflow to sub-parsec
scales. The efficiency of this process hardly depends on details, such as gas
temperature, initial virial ratio and power spectrum of the gas distribution,
as long as it is not strongly rotating.
  Adding star formation to this picture might explain the near-simultaneous
formation of the S-stars (from tidally disrupted binaries formed in plunging
gas streams) and the sub-parsec young stellar disc around Sgr A$^{\!\star}$.
