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A small shed on a carport requires power for 1 power point and 3 lights. I don't know if the owner prefers overhead or underground cable route yet for the 3m gap between the house and shed. Please can someone let me know if there is a minimum cable size to a sub-main? From 3.12.2.2 it looks like 6mm for aerial.

3.12.2.2 Minimum size
The minimum size of aerial conductors shall be as follows:
(a) Copper and aluminium conductors Copper or aluminium conductors installed as aerial conductors shall have not less than seven strands and shall be not smaller than 6 mm2 for copper or 16 mm2 for aluminium.

What about underground? Thank you.

Clause 3.5.1 & Table 3.3 set minimum size based on conductor function .
( a look at the index would have found this)

The greater minimum size for aerial is because an aerial conductor needs to be strong enough to be self-supporting.
If you use catenary support, clause 3.12 does not apply; use 3.13 instead

I wouldn't bother running it as a "submain" and having a switchboard for just a few items.
Simply run one RCD protected final subcircuit for everything. Run a 2.5 on a 16A circuit, and reduce to 1.5 for the lights if necessary.
As Alec said, if you use a catenary, it's not classified as "aerial" and those minimums don't apply. But be aware that if you run a catenary, minimum height of 3m is required. To get around this, you can put a fixed support (timber or metal or whatever) between the two buildings and fix the cable to the structure. Or go underground if they don't want the eyesore.