Do common grounds lead to current flow?

[TSG_tesla]

Hey guys, this question will probably seem really stupid to some, but do common grounds lead to current flow between them?

I'm building a full room lighting setup, all controlled by one arduino, wicha is connected to my PC via USB. The LEDs are getting powered off a 4pin molex connector from my PC powersupply, the Arduino via my USB port and some LEDs are using an additional 12V 5A source.
Since they all hav different potentials (from my understanding) I would have to connect the grounds together, to get a clean digital signal from my Arduino, but the difference in potentials between the grounds would lead to current flow, wich would even out"" the voltage levels (I hope I got that right...).

Now, is there any danger, or do I have to protect any components aginst overvoltin when doing such a setup? Would the ground wires heat up, since the PSUs are relatively high current??? (5-15A)

Any suggestions, answers are appreciated...

heres a Link to the circutry of my setup: http://prntscr.com/gud6wg

 

[duke37]

Draw a loop for each supply, You will see that D2 takes its corrent from the Molex and the only current in the ground wire will be the data control current. Likewise for D3. This current will be very small going to the common ground point. Each loop may have a high current but most of it is contained in the each loop.

The current capability of the power supplies is irrelevent so long as the supplies are not overloaded.