There once was a super powered moa, and comic book Superman did battle with it and managed to capture it unharmed just near the end of the issue. What did Superman do with the beast?
This is Action Comics #425 - "The Last Moa on Earth".
Strange gases affect the last moa egg
The moa drains the hunter's life forces, growing to an enormous size within hours
Superman fights the beast which can now fly and has become psychic.
Before finally realising that the animal simply wants to go home
Since there are no further mentions of this animal, I think we can assume it lived the remainder of its life in peace and tranquility near the pond
It's most probably in his Fortress of Solitude
Superman has a handy Interplanetary Habitat area in his fortress. He's such a good guy, he can't just kill every super powered creature he battles, so they usually end up here.
I'm unable to find a specific reference to the moa in question, but he's very likely here.