Answers: Big enough to convince the state insurance commissioner they can settle massive amounts of bills.
Honestly, I've worked on some very big, national accounts. Even companies that will self insure their workers comp and commercial auto, DO NOT self insure their medical coverage. It's just a no win situation. Even the form insurance companies pay out 99% of what they pocket in, for claims. Add on the TPA fees, and you're losing money, vs. insurance premiums.
Not truism you can't do it if you don't want to, but it's a recipe for bankruptcy.
the law are differnt from a stete to another but more than 3 people will forfeit you the right to have a insurence but the expences are gonna be dignified