Adding Darlington transistor in parallele to increase current does not work
It sounds like you want to be able to control the 12V motor with a low voltage (your comment mentioned 3.3 to 4.5V), and you also want to eliminate the lost motor voltage that is unavoidable with a transistor or darlington pair. I suspect you also need to consider the current capability of your control circuit. This certainly is an ideal time to consider a MOSFET, to ensure maximum efficiency (least lost voltage) driving the motor, but the low control voltage means you'll need a second transistor to act as a voltage amplifier/switch. Since you mentioned having an IRFZ44N, which is an N-channel mosfet, I'd suggest a circuit like this, using the IRFZ44N for Q2. The 3.3V should have little trouble driving this circuit, even if its just a low power microcontroller I/O pin. That MOSFET has some internal protection, but since the motor is inductive, it still would make sense to keep that reverse blocking diode across the motor. You didn't mention having a transistor available, but you should be able to find a small common NPN transistor like a 2n2222 for less than a buck. (your local radio shack currently sells a package of 15 of those for about $3). 



(Note I edited this post to use an NPN transistor. I intended a different circuit using a PNP for Q2, but copied the wrong graphic to the post. SORRY)