For thousands of residents of South Los Angeles who had depended on the large county-run King-Harbor hospital that closed in 2007, the past 10 months have been an exercise in cobbling together medical care. When King-Harbor was shut by federal officials, it became the 15th general acute care hospital to close in Los Angeles County since 2000. South Los Angeles continues to be one of the most difficult places in the nation to both receive and give medical care. Family doctors are few and far between, and the area is one of the hardest to draw new doctors to, physician recruiters say.