LLMs and the Obscene Publications Act, theoretical question

Not a specific question and I don't want to generate this stuff nor am I a law student - more curious about what the law is on this.

As I understand it, an obscene publication needs to be published and obscene (the definition of which isn't entirely clear, but things like descriptions of child abuse or incest would certainly come under it) and both publisher and the person requesting it can commit this offence.

How does this stand with LLMs?

1. If I ask for something obscene from an online LLM, I would be committing an offence, but would the model hoster also commit an offence and how would this be dealt with?

2. If I ask for legal output and it returns something obscene without me explicitly asking for it, would I still have committed the offence?

3. If I use a local LLM so nothing is transferred and only I can see it, is it still illegal?

4. If I download an LLM which has been fine tuned to generate something obscene (and labelled explicitly as such) and I run it locally, have I committed an offence by downloading the model?