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cdru
You can run multiple wires to share the current. Presuming the supply and ground are the same gauge, you'll need just as many ground wires as supply. A single larger gauge wire may be easier to route and provide more flexibility than a bundle of smaller wires.
If you run all 4 traces in parallel, and each trace is .85 ohms, then your overall resistance is 1/4 that, or .2125 ohms. To keep the resistance at .85 ohms, you'll need to wire it so that pairs are ran in series and then each pair is ran in parallel.
If you're worried about the aesthetics of having all the wires, you can open the supply (unplugged of course) and clip the unneeded wires inside the case. Just wrap them in a bit of electrical tape to make sure they don't accidentally contact the case or each other and they are out of the way.
Ah! This may be the solution I'm looking for! I'm not picky about the aesthetics, and where I have to run multiple wires between, for example, the heatbed power connection on the board to the PSU, I've some nice black heatshrink to keep the multiple wires together.
So from what I can tell, the plan is to take 3 x 12V wires and 3 x GND wires from the ATX and "group" them so that they all connect to the HB + and GND respectively.
Then take a single +12V and a single GND from the ATX and go to the board power (for all the other stuff)
and then one last +12v and GND for the fans.
With the other cables in the ATX, I've the ATX case open, and they will all be cut short, and heatshrink put on the ends of them so that they'll be neatly bundled off INSIDE the ATX case.
That all seems ok, right?