What's the maximum power capacity of a transformer with super conducting wire?
Assuming the core is at room temperature, the core will saturate at the same magnetic field with or without superconducting wire. The only thing you're saving is the copper losses. 

However, if there was no issue with critical current density \$J_C\$ of the superconducting wire, the core would not be necessary and the transformer could operate as an air core transformer at unlimited power. It would draw enormous magnetizing current. 

In practice, the critical current density of the wire would be exceeded, it would go normal, and the thing would go phhhhht.