What does the animal hospital do with a dog's ashes?

Depending on the veterinary hospital, most use an outside service for cremation.  The hospital should have no problem giving you the contact information for the service so you can personally speak with them about the subject.  Most offer communal and private cremation services.  With private cremation, your pet is cremated by itself and you recieve only his/her ashes.  With communal cremation, all pets are cremated together.  What happens to communal cremation remains depends on the facility.  I would suggest contacting them personally to find out the details.  Allied Cremation Services in Palmyra, PA is an excellent company and they are always wiling to answer questions about the service.  They've even allowed owners to be present for their pet's cremation.