jd47 - it is not ok to connect different type of devices to the same power supply because they have different impedances and loads. Some loads are reactive other inductive or capacitive, so I dont recommend you to use the same 12v adapter.

Try to use a higher voltage transformer, then a bridge rectifier with diodes and finally 3 voltage regulators like 7812 to power up each line.
The best way is to use 3 transformers for each line but this is my opinion.