Port size or Supply for Naval Upgrade/Repairs?

[Feinder]

Several of the Australian and New Zealand ships start of a partial strength (along with the UK Eastern Fleet).
I haven't been able to repair the Australian ships fully, at any port in Australia (including the big-ish one in the SouthEast).
I can send them to India. I can send them to US and UK.
At this point, I'm experimenting ("What conditions do I need to upgrade/repair my ships?").

1. Does the size of the port have any impact on the ability to upgrade or repair a ship? There are plenty of usual Size(5) ports. But there are a handful of Major Ports, with size(8) or more. Is there any advantage to using a major port?

2. From my tinkering, it looks like it's more likely based on the supply of the city at the port, to allow Upgrades and Repairs.
A. What is the minimum supply required to upgrade a ship?
B. What is the minimum supply required to repair a ship to Strength(8)
C. What is the minimum supply required to repair a ship to Strength(9)
D. What is the minimum supply required to repair a ship to Strength(10)

And yes, I get the part about, "You can't repair a ship by more than 5 strength points in a single turn."
But I'm fairly certain that I also tried putting the Australian HQ in a port-city (thus 8 supply), but I still couldn't repair my ship past 8 strength-points.

[ElvisJJonesRambo]

@Feinder --- You are correct. The Aussie (*disclaimer, not derogatory) and Kiwi (*disclaimer, not derogatory) ships (*and boats, don't want to leave them out) need to travel to India or any a port that is > strength 5. That is, if you want to max out the naval unit to 10.

[petedalby]

My understanding is:

At port strength 5 or more you can upgrade your ships.

At port strength 5 you can only reinforce ships up to 8.

At port strength 6 or more you can reinforce ships to 10 and also gain Elite Reinforcements if available.