Thanks for the info everyone. We saw the mosquito flat campground last year when we drove up there to go to Pie in the Sky Cafe. It was raining, so it was empty, but we thought that'd be a great place to stay sometime.
Odd question, but as far as 'claiming' a campsite, what do you do? Set up your tent, then go for your hike? HM is a pay site, so I assume you fill out some paperwork or something, but Mosquito Flat is free.
Is it fine to setup multiple tents on one site? I know Onion Valley has a limit of 6 people per site, but I don't see any restrictions on Mosquito Flat or Cottonwood. Does 'single unit/site' mean 1 tent per campsite?