If a transfer is not accepted or rejected within 72 hours the pet will be returned to the account that sent it. This can take a bit of time so please be patient and don't panic if your pet isn't back as quickly as you anticipated. This also applies to transfers sent to an account that no longer exists.
If you sent your pet to an existing account and they accept it, you will have to contact the owner of the account to have the pet returned. They are not under any obligation to do so so please be very careful when typing the username you want to send your Neopet to through direct transfer!