ULA has a great writeup of how you might do this if you have on orbit refueling capabilities.
And on the one hand it seems like total science fiction but on the other, Elon is talking about next year.
In fact, a permanently-in-orbit transfer vehicle might make sense here; have this vehicle run the actual Earth<->Mars transfers, then just shuttle in fuel/supplies/crew on each Earth arrival.
Either way, a Falcon-like reusable launch system makes plenty of sense here in terms of making this sort of thing possible.
Buzz Aldrin is a big proponent of this approach: https://buzzaldrin.com/space-vision/rocket_science/aldrin-ma...
Evidently this problem is solved, because liquid fuel rockets have been working fine in space since the 60s. (Liquid fuel rockets have their propellants pumped into the chamber.)
> nominal bleed off from warming
Launch the tanker just beforehand. There won't be time for the fuel to bleed off.
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.
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.
The idea of docking modular components in space is a good one though. Perhaps all you really need to do is lift a bunch of fuel tanks since there is plenty of time to perform burns with smaller boosters on longer distance trips.
Worse, the extra steps involved create extra risk, both for mission failure and to the lives of the crew. You could get to your fuel depot and discover the battery sytem has failed and your depot is tumbling, or a leak caused ice buildup that prevents you from docking. Or the chillers failed and enough oxydizer got vented into space that you can't continue the mission.