AC/DC “High” Voltage

While it's common practice on schematics for small (i.e., all in the same place) circuits to show grounds that don't appear to be connected, this is just a convenient way not to clutter up the diagram with all the return paths.

If however you're talking about literally kilometers of physical ground, you'll find that in practice, at least with power delivery, there is always (afaik) a return conductor to ensure a low impedance to complete the circuit. In effect, this return conductor is in parallel with whatever conductance the actual earth connections afford, so some of the current will actually travel through the earth, but mostly it's going to be found in the wire.

RF applications might get away without this return wire, but then RF applications can oft times get away without either wire, so I'll leave that aspect for someone else to tackle, should you be interested.

The wire gauge you need is a function of several things.

• The acceptable voltage drop or power loss (that appears to be the only thing considered in the website you linked). The voltage drop (and power loss) is proportional to wire length and inversely proportional to the cross-sectional area of the wire- in other words inversely proportional to the square of the wire diameter (assuming constant current).
• The acceptable temperature rise. This is a function of the number of current-carrying wires bundled together, the environment (maximum ambient temperature and air pressure or altitude, for example), the insulation type, the wire type (some types of wire are plated to withstand higher temperatures than bare copper without corroding).
• Regulatory requirements and other considerations- for example, the wire may be rated for 200°C insulation, but you might not want the wire to run that hot.
• Fusing- the fuse or circuit breaker should protect the wire in the case of faults such as overload or short circuit.

Very short lengths of wire can depend on heat sinking through the ends (indeed, in a vacuum, that may be the main heat loss mechanism), but usually that's not taken into account.

Normally you'd run through a checklist such as the above to make sure ALL the requirements are satisfied simultaneously, so you might find that using PTFE insulated wire allows you to use AWG 18 wire, but because of the voltage drop limitation you'll have to use AWG 12 wire.