I think we debate about the validation of circuits laws (KCL & KVL) when the circuit will be included of superconductor. The circuit current just limited by source internal resistance in DC condition. 
For AC condition, you can suppose a current transformer with super conductor secondary winding. When secondary side of this CT is shorted without any additional load, as Claude said, the leakage inductance of current transformer limits the secondary current. In this case we front the inductance drop voltage ( L*di/dt ) against secondary induced voltage as emf of super conductor closed ring which made induced secondary current. 