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Basically, when you start undoing the nut that connects the radiator to the system, nothing will come out because the bleed valve is creating a vacuum.
As you undo the bleed value, the water will start pouring out the side that you've undone.
so it's a balance between how much the bleed valve is open and how much the retaining nut is open as to how wet your carpet gets :)
TLDR: have access to the wrench at all times in case you run out of places to put the water.
Good shout on the wet vac, have a screwfix voucher so may go that route. Although I'm sure either way I'll be getting in a flap. Just to check, you're talking about not fully undoing the cap nut during the bleeding process to reduce the rate of water escaping? Obviously this has to be fully undone if removing the rad.