Any ideas on what size pot I can eeplant my beast of an aloe vera in?

Very cool form! An Aloe, but I'm not positive it's an A. vera, and that growth habit might dictate the size and shape of the pot. Looks pretty happy as is.
We have several Aloe experts —
@Baja_Costero, can you advise?

Yes, it is not Aloe vera but another of the hundreds of species of aloes. It could go in a 3 gallon (10 inch/25cm) pot if you like. Make sure the new pot has holes at the bottom, and use soil with good drainage (eg. 50% pumice/perlite/gritty equivalent).

Up to you of course, but I'd be tempted (and especially if it turns out floppy) to prune and root the tall part. It'll be 'fun' finding out how it comes out of that bowl. I think we'd like to see that, after repot, if you don't mind.

Right. "Fun." 😳

I'd be tempted to break the bowl rather that attempt to pull the adults and pups out through the narrow opening without damaging them.

How big was the original plant? It looks like there is no drainage, yet that Aloe is beautiful and obviously healthy. Good job nurturing it!

It looks so happy! I would cut & root the tall part too, and leave the rest of it alone.

But putting that aside, an unglazed clay pot is always awesome for me because I like to water often. That may not be a positive for you because you obviously have great watering restraint to keep a plant alive for so long in a pot without a drain hole.

Thank you for all your comments. When I first had the plant, it was about 2 inch's in height. I was concerned too about drainage, so I planted another one in a terracotta pot with drainage and its tiny compared to the one in the bowl. As the plant does seem happy, and I am totally inexperienced on repotting and root trimmings, I think I will leave well alone as the last think I want to do id kill it

Happy to reply. The only risk in cutting off part of it is to the removed part. The rest of the original plant will be indifferent to that.

If you have an interest, you would cut somewhere, remove a few of the leaves closest to the cut end so there is some bare stem. Then let the wounds heal by leaving it unpotted for a couple of days. Then stick the bare stem part in a pot. Might need to put a few small rocks around it in a circle so it doesn't fall over while it is making some roots. With such healthy material as your plant, it should go well. If you don't want to, there's no reason you should. Just that you could if you did want to.