I recently accidentally drained the battery on my car while I was fixing unrelated stuff on the door (and therefore had the door open for 3 hours). I bought a "jumpstarter kit" which is basically a 12000mAh LiIon battery (3.7V) and some electronics. It's just a little bigger than a large mobile phone, but you clip it to the car battery and it's capable of providing 12V at 600A to turn the starter motor for up to 5 seconds. That's 7.2kW from a shockingly small device. I treated it with all due respect.
1. It’s unlikely there’s power conversion circuitry in the kit. It’s almost certainly a few cells in series.
2. I’d be surprised if it can actually produce 600A at 12V. It’ll be “12V nominal” into an open circuit, which is really more like 14V for a 4-cell Li-ion setup. But even a 600 cold cranking amp lead-acid battery only supplies 7.2V at 600A.