I'm certain if I drew a cartoon and used the signature that looks just like a real cartoonists', I would get sued and liable for the damage.
The same should apply to LLM vendors.
If you publish it, no issue in drawing anything for personal use. Same with AI One who published will be liable.
Laws are for poor people
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Not unless you actually tried to sell it for money.
If you just draw a cartoon with a fake signature, nobody is coming after you. Even if you posted on Twitter or something, nobody is coming after you.
You'd have to be fraudulently selling it in a book of cartoons or on coffee mugs or something.