>How would an out-building (shed,garage),
>be supplied with Electricity, in your
Underground or simply clipped to a wall or other reasonably secure part of the building. In the latter case "romex" style EKK could be used. I have to admit that I don't know which is the common way today.
(The garage at my parents house is supplied with an old "romex"-style cable on a fence. I had an electrican in to have it replaced, as the outer sheet has disintegrated, but in his opinion it was in good condition. If it failed completely, the RCD would trip, preventing any danger.)
>Is it required to be run underground
Over-head is only used by PoCo's.
>what type of cable is required in each case?.
Aluminium "armoured" underground cable is very often used as general purpose wiring for 4mm2 and up. Therefore I would think any underground wiring is carried out with this. In theory, you are allowed to use ordinary aluminium sheated cable provided that it is protected from mechanical damage. If you go through the trouble of U/G, I think you'd drop at least a 5x2.5mm2. (There is little money to save on using a smaller cable)