According to this,
How big could a black hole get
recent studies suggest that UMBHs cannot physically grow much beyond this (10 billion solar masses) anyway, since they would then begin to disrupt the accretion discs that feed them, choking the source of new material.
I don't understand this. What would happen exactly with the accretion discs if the UMBH grows beyond 10 billion solar masses? How would the accretion discs be disrupted by the black hole?
The article you cite is almost certainly referring to the suggestions put forward by King (2016), Inayoshi & Haiman (2016) and Yazdi & Afshordi (2017), that there is a limit imposed by gravitational fragmentation of any accretion disc feeding the black hole.
Black holes are generally fed by gas, in an accretion disc, losing energy and angular momentum, until it reaches the innermost stable circular orbit (ISCO - a feature of General Relativistic orbits). Further loss of energy then results in the material falling rapidly to the event horizon.
To grow a black hole at a significant rate requires that the average mass inflow is roughly equal to the mass of the black hole divided by its age. The bigger this value, the more gas there must be in the accretion disc to accomplish that accretion rate.
However, if the disc is too massive, it becomes "self gravitating" and can begin to fragment and form stars (it breaches the so-called Toomre stability criterion). If it does so, then because orbiting stars do not lose energy or angular momentum anywhere near as easily as hot gas, they won't necessarily fall into the black hole and its mass accretion rate is drastically reduced.
The big idea here is that, when you do the maths, the discs become self-gravitating beyond some outer radius. If that radius become smaller than the ISCO then you cannot get a stable accretion disc to feed the black hole and it stops growing (at a fast rate).
According to the papers above, this occurs at around 50 billion solar masses (but maybe 300 billion solar masses for the fastest possible spinning black holes). Above this limit, black holes could not be accreting sufficiently to grow their masses on timescales of the age of the universe. i e. They could still grow, but only very slowly.
Also note, that this limit applies to luminous accretion from a gaseous disc. It would still be possible to grow these black holes by mergers with other black holes for example. But there is then an observational bias against detecting such black holes, until perhaps we have a low frequency gravitational wave detector in space.
