We can't have walk up vaccinations with no previous sign up. People will wait in their cars for 8 hours to get the shot. We have seen pictures of that happening.
States know by Tuesday how many doses they will receive for use the following week. They also know how many doses they have on hand. In Oklahoma they set up the scheduling portals and open up sign up on Wednesday evening. The state sends out emails to those eligible for that weeks sign up.. All slots fill within hours. If more doses are received than expected they add additional slots.
Slots are limited since Okla has only been getting 30,000 to 40,000 doses a week, about 1% of the population.