Florida has approved 14 companies to take over 301,563 policies from the state-backed insurer Citizens Property Insurance Corporation. Citizens had become the state’s largest insurer with 1.2 million policies, prompting legislative efforts to reduce its size. Clearwater-based Homeowners Choice had 18,000 policies — all from Citizens — in September and recently more than doubled that with 45,000 Citizens policies. The approved companies are required to offer the same or better coverage at the same or lower price. The insurers benefit by avoiding some marketing costs in their effort to grow, while the state cuts its risk.