I am registered as the dog's owner on Vets Records, Vaccination Record and Microchip certificate. All he has is the bit of paper from the Dogs Home. The dog was always intended to be a companion to my existing dog (that was brought with me into the relationship) and therefore at best you could argue the dog was joint.
If you are registered as the dog owner with the vets and on the micro chip and you are currently in possession of the dog, I would say are holding the winning hand