O27 (and other 3 rail O systems) generally use variable AC transformers. The motors can run on either AC or DC, and are reversed through a sequencing system. If you use DC, polarity does not matter. Turn the throttle off and then on sequences to the next step. Most sequencing is forward-neutral-reverse-neutral-forward. There are a very few O27 trains that omit the neutral from their sequence. Train speed is controlled by varying the AC voltage.
The 2 rail systems use DC-only motors, and are reversed by changing the polarity of the rails. Again, train speed is controlled by varying the voltage on the rails, in this case DC. DC power supplies are commonly called "power packs", not "transformers", becasue they contain a transformer (to reduce voltage from household 110 to 16 or so, a rectifier to change the power from AC to DC, and a control to vary the DC voltage on the track.
In both 2 and 3 rail, common ground is used to simplify wiring for multiple transformers and multiple trains. But you still must electrically isolate sections of track, called blocks, and assign the block through an electrical switch to one transformer/power pack or the other. You do not want to have 2 transformers/power packs attempting to control the same block of track at the same time; it doesn't work! You tend to either get a runaway engine or shorted power supplies!
In your case, you can use mulitple AC transformers with your 3 rail system by connecting the U posts together and to ground (usually the outside rail). The only caution is you must "phase" the transformers. The best way to do this is to hook a wire to the variable post of the two transformers you wish to phase, turn each transformer up about half way. Touch the two variable post wires together. If there is no spark, or a very small spark, you are already in phase. If the spark is larger, reverse the wall plugs of one of the transformers, and you are now in phase. Once you have the transformers phased, mark the wall plugs with a marker so you know which way to plug them in.
You can also use a common ground in DC provided each power pack has its own internal transformer. Common ground wiring used to be recommended for its savings in block toggles becasue you needed one less pole on the electrical switches used to control the blocks (or sections) assigned to each power pack. However, if you someday switch to DCC, an electronic control system for 2 rail DC, and use more than one control section, you cannot use common ground (more appropriately called common rail). Also, certain types of turnouts (track switches) in 2 rail (but not Atlas) force you to cut gaps in the common rail anyway.
Probably too much information here, but without knowing the details of your situation (2 rail/3 rail and/or AC/DC) it's hard to tell from your first post what situation applies to your common ground question.