What matters is your total copper cross section and the trace length. Both of these numbers contribute to the total resistance of the trace (if that's important) and the resistance per unit length which contributes to temperature rise (if that's important). If it's a DC current, there are no issues that I can see. For higher frequencies, you might be generating magnetic noise if your return trace is farther away. (Magnetic noise is proportional to current x current path loop area)
Here is a website that can help you calculate the total amount of copper based on the target temperature rise: http://circuitcalculator.com/wordpress/2006/01/31/pcb-trace-width-calculator/
Edit:
Another way to go on the cheap side is investigated by Dave Jones and Mike:
EEVblog #317 - PCB Tinning Myth Busting (14 minutes youtube video)
Does putting solder on high current PCB tracks help? (4 minutes youtube video)
Basically, leave your trace open on the soldermask, then go over it with a LOT of solder to beef up the trace cross-section. Another possibility is to just use a big fat wire to jumper it across your PCB.
They are using power planes, maybe even with double-thickness copper layers too (70 microns / 2oz, rather than the usual 35 micron / 1oz Cu thickness), so the power path to the outputs is not going to be high resistance, and therefore not waste much power as heat loss, and therefore will not get hot and explode and otherwise be unable to "handle" the amount of current shown.
120A for 8 outputs is not too bad, each contact (which looks like just exposed mask on copper planes with holes for thermal relief) only needs to handle about 15A each which is entirely possible with nice fat wires going out to the rest of the set-up.
I would be worried though, first about the size of the battery needed, and second about your safety, if 120A loading was a common thing in your system.
You must also understand that using a trace width calculator makes certain assumptions, for example what the ambient temperature is, what the acceptable rise in temperature of the traces is, and in some cases how long the trace is, and finally the thickness of the trace which is usually measured in micrometers or ounces/square foot (oz). If you allow up to 30-40 degrees Celsius increase in temperature of the traces (which is usually fine for power related systems, which are often rated to 120-150 degrees) you can get away with very thin (2-3mm) tracks for carrying 15A, let alone how much you can do with a whole power plane (could be modeled as a 30-40mm wide trace!).
Best Answer
You'll need it wide, and thick if you can (2 oz copper vs 1 oz copper). There are calculators like this one https://www.4pcb.com/trace-width-calculator.html that take into account current, copper thickness, allowed heat rise, internal or external trace, trace length into account and calculate a trace width. Other board houses have calculators also.