The effect on Nazgul as couriers of the One Ring

Question

This may probably all be speculative, but what effect would the One Ring have upon the Nazgul, who each wore a ring of power, if they had indeed captured it during the hunt for the Ring?
Would the Ring move itself to be found/worn in a similar fashion as it had done with Smeagal/Gollum and Frodo, or, as the Nazgul were already in Sauron's service, would there likely be no effect at all?

Answer 1

The Nazguls' minds and wills were captured and enslaved by Sauron, who retained their rings, so there would probably be no other effect than them immediately bringing the One Ring directly to their master.