Tampa General Hospital and Florida Hospital are teaming up to build a $60 million outpatient center in Brandon, launch a home care agency and create a hospice program. Their jointly owned partnership, called West Florida Health, is driven by a changing health care economy that favors big systems that can care for patients at all stages of sickness and health. Top officials from the two nonprofit hospitals provided for the first time Friday the details of their partnership, announced in September 2013. Officials were careful to say the partnership is not a merger of hospital operations.