You've mentioned in the past that the 380's brakes get very hot just taxiing. Is there a limit to the towing of the 380? Is it limited by the brakes of the tow tug? Can it be towed only with engines off? Any other restrictions on distance / weight? Are the tugs purpose designed or adapted from existing 744 / A330 equipment?
The aircraft brakes are not used at all when being towed. Depending upon the aircraft type, the hydraulics will be partially powered up, to pressurise the braking systems, as a last resort, just in case the tow bar breaks. I can't think of a time when an aircraft would ever be towed with an engine running, other than the occasional 'pull forward', after being pushed from the gate, as the crew are starting the engines. Having said that, depending upon local rules, and the particular tug in use, you may not be able to start any engines at all until completion of the pushback. Each running engine is going to provide about 8,000 lbs of forward thrust, even at idle, so you'd run the tug out of brakes pretty quickly. On a wet day, the smaller tugs used domestically can run out of traction with even one 767 engine running.
I don't know the overlap of tug usage. Obviously the biggest are used with the A380, and I expect the tow bar variety can push any smaller aircraft (which is all of them). QF bought some new tugs of the type that lift the nose gear for the 380s, and they're used in LA. I used a similar type (at various locations) when flying the 747, so I expect they can be used with any of the bigger aircraft.
The dynamics of a tow are quite different to a taxi. Firstly, the aircraft will normally be a lot heavier...there's not much reason to tow with a full load. Speeds will be higher when the aircraft is under its own power (up to 30 knots), and the aircraft may have an appreciable distance to travel. And, that previously mentioned idle thrust will be there...but now with all of the engines providing a share. At some airports, where the surface isn't level (i.e. Melbourne) you may have a considerable downhill run, and that can make a huge difference to just how much you have to brake. The normal technique is to let the aircraft accelerate up to the max speed, and to then brake it back to a slow speed. You don't ride the brakes in an attempt to hold a constant(ish) speed, as that will put a lot more heat into the brakes. If you aren't careful, you can easily put a hundred degrees C into the brakes whilst taxiing out to the runway (long taxi, hot day, heavy weight). There is a limit of 300 degrees for take off.
That limit isn't a problem from a cold start (when the aircraft has been on the ground for some hours), but departures from Singapore and HK both occur about 60-90 minutes after arrival, and the brakes will easily hit 500 degrees after landing. So, leaving the terminal, the temperatures could already be around 200 degrees...