Indeed, graphene seems capable of .99 of black body radiation limit.

Quote: "emissivity higher than 0.99 over a wide range of wavelengths". Article title "Perfect blackbody radiation from a graphene nanostructure" [1]. So several rolls of 10 x 50 meters graphene-coated aluminium foil could have significant cooling capability. No science-fiction needed anymore (see the 4km x 4km NVIDIA fantasy)

[1] https://opg.optica.org/oe/fulltext.cfm?uri=oe-21-25-30964

Aluminum foil of great surface will not work very well, because the limited conductivity of a thin foil will create a great temperature gradient through it.

Thus the extremities of the foil, which are far from the satellite body, will be much cooler than the body, so they will have negligible contribution to the radiated power.

The ideal heatsink has fins that are thick close to the body and they become thinner towards extremities, but a heatsink made for radiation instead of convection needs a different shape, to avoid a part of it shadowing other parts.

I do not believe that you can make an efficient radiation heatsink with metallic foil. You can increase the radiating surface by not having a flat surface, but one covered with long fins or cones or pyramids, but the more the surface is increased, the greater the thermal resistance between base and tip becomes, and also the tips limit the solid angle through which the bases radiate, so there must be some optimum shape that has only a limited surface increasing factor over the radiation of a flat body.

It's not as exciting as you think it is. "emissivity higher than 0.99 over a wide range of wavelengths" is basically code for "it's, like, super black"

The limiting factor isn't the emissivity, it's that you're having to rely on radiation as your only cooling mechanism. It's super slow and inefficient and it limits how much heat you can dissipate.

Like the other person said, you can't do any better than blackbody radiation (emissivity=1).