In superconductivity, does the diameter of the cable affect the current? In the water tank analogy below, the smaller diameter pipe (B2)
will drain tank A slower than the larger diameter pipe (B1)
We are told that resistance has this same effect on current
the bigger the resistance, the smaller the current
We are also told that superconductors have zero resistance
So using the same water analogy, and connecting two superconducting cables of different diameter to batteries holding the same amount of charge, 
Would they both drain the batteries at the same speed, having the same current regardless of the cable diameter ?

 A: Suppose you replace the water in your tanks with superfluid liquid helium. Now there is no viscous drag so the flow velocity in the pipes is independent of the pipe diameter. This doesn't mean the superfluid flows infinitely fast because the fluid has mass and therefore the flowing fluid has kinetic energy. This kinetic energy has to come from the change in the gravitational potential energy as the fluid flows downwards, so the flow rate is now limited by how much energy gravity supplies.
If we switch to an electrical circuit the analogy carries over. Since there is no resistance in a superconductor the diameter of the wire makes no difference. But again this doesn't mean the current will be infinite as there are likely to be other factors that limit it.
A: There is a critical magnetic field for each superconducting material (if the magnetic field is higher than the critical value, superconductivity disappears), therefore, the current in a superconducting wire is limited, as current creates magnetic field, but the critical current increases with the increase of the wire diameter, so a superconducting wire of a larger diameter can conduct a higher current.
