I own a co-op apartment in NYC with an ex-girlfriend who moved out 20 years ago. I pay and have paid everything. My rights?

sorry, but unless you have a written agreement that says otherwise, she is entitled to 50%.

She's entitled to her share and she may be able to partition.

Dear New York Shareholder: It may not be likely that your ex may partition the cooperative interest, if she has no interest in launching a lawsuit. Since 1988 New York courts have recognized that a partition action may be brought in a cooperative, even though the ownership interest in a cooperative is considered as personal property and even though the ex owns an indivisible interest in the issued cooperative share certificate. A cooperative is personal property. Any transfer invokes the power of the Board. http://www.nytimes.com/2005/11/06/realestate/06home.html?_r=0 Over time, the market value of the apartment likely substantially increased and so would your respective interests in the event you and the ex seek to sell. Unless the maintenance increased in similar proportion to the value of the apartment, your ex made a good investment in buying this apartment with you and allowing you to take care of her ownership interest. You need a lawyer.