I believe the Zero W sales page states to us a 2 amp power supply.
I have read that the zerro will run on as low as 3 volts (not sure what was ment by running ) but they never mentioned the equired amps.
I've a load of old phone chargers ranging from 0.5ah to 1.5ah lying about in the event of an emergency but 2ah is usually what is recommended.
So annoying when you think the Pi is booting with the blinking LEDs when in fact it's constantly rebooting. It's definitely a 5 volt input, no more no less.
The only other voltage mentioned is the 3.3 volt on the GPIO rail which bypasses the regulator and is not recommended for usage unless you're technically minded and know what you're doing.
I use a 2ah battery pack with a regulator on my outdoor Pis.