Liquid fuel rockets use Surface tension against the slosh baffles to hold fuel in partially full fuel tanks in place.

Ullage motors are used to settle the fuel at the bottom of the tanks, so the main motor pumps can get to it.

Once the main motor starts providing acceleration, the ullage motors are no longer required.

For cross tanking, keeping the ullage motors running for long enough to transfer all the fuel, without the main motors running might be prohibitive.

https://en.wikipedia.org/wiki/Ullage_motor

I didn't know about ullage motors, thanks for the link. The link also says that only very tiny accelerations are needed - so this shouldn't be a big problem for a tanker. Like I hypothesized, the problem has been solved.

Bearing in mind that the ullage motors need to be of a type that won't suffer from ullage problems. That implies they cant use the main motor fuel.

The saturn 5 used small solid rockets as ullage motors. Alternatively you could use externally pressurised bladder tanks for a range of non-cryogenic fuels. Cold gas or possibly h2o2 as a monopropellant come to mind. Either option has a comparatively low specific impulse, so even running them at very low overall accelerations for extended time periods is likely to be cost-prohibitive.

I like the suggestion elsewhere of spinning the tank. You could also dock, then spin the whole combination ship. If you abandon the fuel station idea, you could just take the extra fuel tank with you, transferring fuel to your internal tank during a main engine burn, then abandoning the empty tank in a wierd orbit.

it's only been solved if it's demonstrated, which it wasn't.