When a constant current is applied to a battery, its voltage jumps by a huge amount in a moment. It jumps up if we apply constant charge current and down if we apply constant discharge current. I k...
I can confirm that "jump starting" from a bench power supply works for NiMH batteries. Here's what I have tried with AA and AAA NiMH cells: set a bench power supply to a max. current of 1 A and 0 V. Connect the battery. Increase the voltage until the current maxes out at 1 A.
When jumping a car, we connect the + end of the charged battery to the + end of the dead battery, and the - end of the charged battery to the chassis or other metal part of the car. I always thought that you need a closed circuit for current to flow.
Your starter will "automatically" use as much as it needs up to the max. If the starter needs more than those units can supply, the jumper will only provide its max. If your battery is only partly dead, i.e. it won't start, but the interior lights come on, you can use a smaller jumper than if your battery was completely dead (and likely damaged).
Eg. Your car needs 600 amps to start: The 1000 amp jumper can handle it. Your car needs 1200 amps: The 1000 amp jumper can't do it. You'll have to find a bigger one. Be aware that this does not apply to voltage. If you have a 6V battery and you connect it to a 12V source, you can blow the battery up.
The circuitry in the car is also grounded to the chassis, albeit with some other protection in between, but this has nothing to do with the current flowing from one car to another during a "jump." If anything, this circuitry can be destroyed from spikes in the battery voltage.