Common Law Separation

My partner and I lived together for 9 years in a house I purchased on my own. My name is the only name on the mortgage and I alone put down the down payment. Once we moved in together we split all bills down the middle. Now that we have split up, what is she entitled to as far as equity in the house. She feels she is entitled to half but is she since her name is not on the mortgage and she was not involved in the purchase? I am willing to give her back what she put in and double it. Is that fair or is she really entitled to half the equity?