Ron O. Wrong!! Animal control is there to deal with rabid wildlife in people's yards or badass dogs that are also a problem. They don't come pick up owned dogs from their owners who just want to re-home the dog. AHS will do that service but they require the person wanting to give up the dog or cat to call them first and set up an appointment to come in to the shelter.
Unfortunately we are at capacity for animals right now. You would need to call Austin animal center and ask to speak to someone in the pet resource center to set up an appointment for owner surrender. Or you can always try to rehome
Try calling Animal Control to see if they can help you
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