[MurkyLabs]

It doesn't seem like there's a limit to how big they can get just a limit to how quickly they can get bigger due to what's called the Eddington Limit which explains how matter falling into the black hole emits radiation and if enough radiation around the accretion disk builds up, it can overcome the pull of the black hole and push matter away, at least until enough matter is pushed away that the radiation levels fall back under the limit and matter starts falling in again.

[qualeed]

PBS Spacetime had an episode somewhat recently about a black hole which is growing at many (hundreds? thousands? I forget) times the Eddington Limit. And, as far as I remember, it isn't the only one to exceed the Eddington Limit - just the one with the record for how much it exceeded it.

I'll try to dig it up when I'm not at work (or if I remember the exact episode through the day).

[orra]

I remember this episode too. The answer is four thousand times bigger than the Eddington Limit. Blimey!

The episode is called “The NEW Ultimate Energy Limit of the Universe”. https://youtube.com/watch?v=0rzgYzbzq5Q

[zamadatix]

Importantly, the Eddington limit does not apply to black hole mergers, theoretically allowing as much growth rate as you're able to feed in from smaller black holes.

[pixl97]

This said, the final parsec problem isn't solved/understood. We know black holes do merge, but we don't understand what energy is being bled out of the system so supermassive black holes crash into each other in the timeframes we're seeing it occur.

[allemagne]

So then the only theoretical limit on black hole mass would just be how fast you can put matter in black holes and/or merge existing black holes versus how fast the universe expands?

[MurkyLabs]

I'm 100% an armchair physician so take my words with a grain of salt but it seems like according to the math there is no limit to how massive a black hole can get. There are limits on the size of how big and small things can get and how hot or cold they can get, the second part is pretty cool, Physics Explained on yt has a good video on it (he's got a lot of good videos) but I enjoyed this one on what the maximum temperature is in the universe: https://www.youtube.com/watch?v=NVlEQlz6n1k