Can you split power between two voltage regulators?
Paralleling voltage regulators is not a good idea. Don't. Regulators have tolerances. The LM7812's output voltage can be anywhere between 11.5V and 12.5V. And voltage regulators have a low output resistance, the lower the better. For the LM7812 that's 18m\$\Omega\$ (which is not even so good). If one regulator outputs 11.5V and the other one 12.5V there would flow a current of 27A(!). Obviously the device can't handle that, and it will activate its overcurrent protection.  

Some regulators Are better suited for this, however. The LM317 has an adjust input which allows you to control the output voltage more precisely.  

  

The output voltages in this circuit will be closer together than the tolerance on the LM7812. Still, note that series resistors are used to limit current due to voltage differences.

What you probably could do is power different parts of the circuit by different voltage regulators. As long as there's no low resistance path between the power supplies this shouldn't cause problems.