I have been in a relationship with a person close to 4 years, we are not married although that was the goal. I own a piece of property of which I have had possession over a decade. I saved over $100,000 to purchase this property in 2001 as the sole owner. In the summer of 2007 I refinanced and added this person to the mortgage and the deed. This person has only ever paid 15% of the mortgage ( I keep excellent records). This person has moved out this year and refuses to sign a quick deed. Can I file a quiet title action for the courts to decide?

A quiet title action isn't appropriate for this situation. You will have to buy them out or file a lawsuit for partition. You need to speak to a real estate attorney.