Laws about joint possessions, particularly dogs. Please help.?

My ex partner and I parted ways 4 years ago. We had a dog together which I have always paid for vaccinations, vet bills, food, obedience training, microchip etc. However we have had a sharing arrangement for some time. I don't think he really cares for the dog that much as he doesn't take care of him and has another dog which he keeps at his mothers and doesn't look after, i believe it is more about keeping some control over my life as he knows how much I love and care for the dog. I have looked into it and in my state, which is tasmania, dogs are classed as a joint possession such as a tv or couch. I have had the dog completely in my care for the last five months and now he has started being difficult and wanting the dog back again. Does anyone know If I have to let him have the dog after all this time?