The jury is still out and it will depend on numerous facts: local laws (many tbd), ToS, court rulings (tbd), does the result infringe on existing IP, is the writing copyrighted or part of a patent... In the US, iirc, patents by AI are denied.

tl;dr, no one really knows yet and it will change with time

I see a possible contradiction between 2 common arguments I see regarding AI image generation:

a - ip laws don't apply to AI because it is learning from many examples, like a human does (here AI is a human)

b - I retain copyright because I am just using a tool (here AI is not a human)

It does not seem consistent to have both.

Only if you make it an NFT.