OpenAI’s terms of use state that you own the AI-generated output. Google’s terms of use state that the company does not claim ownership over “generate[d] original content”.
In Hong Kong, the consultation paper on the enhancement of the Copyright Ordinance in regards to AI-generated content has stated the following.
“Generally speaking, the duration of copyright for original LDMA [“literary, dramatic, musical and artistic”] works created by a human author is the lifespan of the human author plus 50 years after his death. As for original LDMA works generated by computer, the duration of copyright will however expire at the end of the period of 50 years from which the works were made.”
The University gives you the right to the AI-generated output using HKU GenAI services when it is for the purposes of teaching, learning, work, and research.