"Most to Least to get/steal a pet?"
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Most:

1. Ticci Toby
2. Puppeteer
3. Laughing Jack
4. Eyeless Jack
5. Bloody Painter
6. Homicidal Liu

Least:

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Ticci Toby & Puppeteer: Okay, Toby probably never had any pets when he was growing up, and not only that, he has a huge soft spot for cute animals. You don't have to ask him twice if you could have a pet. Puppeteer probably had a dog while growing up, so he kinda still has a soft spot for animals. I mean, if an animals gives him those puppy eyes, it's his now.

Laughing Jack & Eyeless Jack: LJ clearly never had a pet in his life and probably can't take care of it either. If he does happen to get/steal you a pet, it's basically your responsibly now since he doesn't know what to do with it besides that it was cute. EJ has a soft spot for cats but he wouldn't steal it, unless it was a homeless cat. Any cat he sees, he wants, so you'll be coming home to a lot of cats...

Bloody Painter & Homicidal Liu: Helen is a responsible person and wouldn't steal the animal. If you wanted a pet, he'd ask you what you'd like as a pet. He'd pay for the animal and give it to you as a surpise. Homcidial Liu is the same way. He won't steal a pet either and would take you to a pet store so you can pick out the prefect animal for you.