By law, the single payer covers every legal resident. The coverage is financed by tax revenues, which are as progressive as the province cares to make them, so it can be affordable for everyone, and in Canada, in fact, it is. Since all providers are in the plan, by definition, there is free choice of providers. For the most part, it's based on an indemnity model. You go to see your doctor, you and the doctor decide what needs to be done, the doctor sends the bill to the single payer.
Utilization review exists but with a light touch.
Basically, they look for patterns of billing that suggest fraud or malpractice. They can do this easily because all providers' billing records are in a single database. Where they do most to control costs is where the greatest costs are located, that is hospital care and particularly high tech procedures. Hospitals are put on an annual operating budget, with a separate capital budget. Hospitals can't compete to have the most high tech equipment, and they don't all need a maternity ward, etc., because the single payer figures out what capital resources are really needed for the province, and authorizes only those.