I'm curious about this so I'm wondering if anyone already knows the answer: What happens to a pet if you give it to an account with no available pet slots in the current system? Would they get a chance to clear a space for the pet or would the first person be barred from the action in the first place?

I looked around for an answer, but was out of luck. :/

You cannot accept a pet if you do not have the slot available, so the pet will stay on the original account until accepted or abandoned.

So does the prompt to accept the pet still pop up for the receiving account if the pet is offered and just an error appears if the account is full on clicking Accept, or is the sender unable to send the pet at all if there are no available slots on the receiving end?

You can send the pet whether or not the user has slots, they just can't accept it unless they have room, an error will pop up and the pet will stay in the original account until they accept (with the slot) or reject it :) Hope this helps.

[edit] Just tested, I have a few pets in limbo until I get slots, I'm currently using all of them and accepting a pet gives me this error:

Thank you! Exactly what I wanted to know. Sorry if the question seemed silly. xP

Not silly at all, you're welcome ^_^