I myself wrote this to earlier query on the same subject on 12/12/2014 now I remember.
Different APUs are fitted depending upon MSN of the aircraft. I am giving below from FCOM. However my experience is APU auto shuts down with batteries off,
Applicable to: MSN 0185-0249, 0264, 0384-0400, 0724
The APU may obtain power for starting from the aircraft's batteries or normal electrical system, or from ground service.
Applicable to: MSN 0138-0148, 0138-0148,0148- 0255, 0148- 0255, 0497-0557, 0932-0943
The APU may obtain power for starting from the aircraft's batteries alone or in combination with the external power, or from ground service.
Applicable to: MSN 0250, 0301-0335, 0440, 0758, 0976-1818
The APU may obtain power for starting from the aircraft's batteries or normal electrical system, or from ground service