Same-sex couples in Tucson can register their union during an event Tuesday celebrating the city's new domestic-partnership law. Tucson's Domestic Partnership Ordinance, which goes into effect Monday, creates a registry for unmarried couples who share a relationship of mutual support and commitment. Registering entitles partners to have visitation rights in Tucson when one partner is in a health care facility, as long as the patient consents. It also extends use and access of city facilities to a person's registered partner. Couples must affirm they are not blood relatives and are not married or in a domestic partnership or civil union with another person. They must share a primary residence with each other and intend to remain in a relationship for the indefinite future. Notaries public and registration forms will be available at Tuesday's event in front of City Hall. The cost to register is $50.