For questions about the process of site graduation, which is when a site moves from the beta stage (where a site's scope is defined and the user base is grown) to a full-blown member of the Stack Exchange network. For graduated sites themselves, use the tag [full-sites].
Use this tag for questions about the processes of site graduation, which the two-phase process by which a Stack Exchange site in beta moves to being a full member of the Stack Exchange network. For questions about graduated sites themselves, use the tag full-sites.
There are two phases involved in site graduation:
Phase 1: Removal of "beta" label and moderator elections
When a site meets the criteria for graduation, the "beta" label will be removed and the site will be placed in a queue to receive a design. Additionally, a moderator election will be held to determine a new, permanent set of moderators; the pro-tem moderators who served during the beta will lose their privileges unless they nominate as a candidate and get elected. Also, the site can become a candidate for a selectable migration path from other sites.
At this stage, the site is referred to as a "non-designed" site as it still has the same (usually generic) design it had back during the beta phase. Privilege levels also remain unchanged from the beta phase.
Phase 2: Design and increase in privilege levels
While a site is "non-designed", the SE team will work out the details of the site's prospective design (i.e. the header image, the theme colors, the site logo, and the badge icons). Once the design is ready, it will be deployed to the site, and it will have a full design.
Also, the site's privilege levels will also be increased to the standard levels used for large sites (i.e. "designed" sites), and the site can now have its own migration paths to allow normal users to vote or flag questions on the site for migration.
What are the criteria for graduation?
Beta sites that consistently get at least 10 questions per day will be considered for graduation and move toward Phase 1. Phase 2 is dependent on the site's overall health and the capacity of the design team at Stack Exchange.
Originally, sites would strictly be in beta for 90 days, after which they would either fully graduate or be shut down. However, later on, SE began allowing sites to have longer public betas; at that time, SE staff would evaluate graduation on a subjective basis, based on whether or not the site has reached "critical mass" (i.e. become large, with many posts and many participants), as well as the capacity of the design team. (Graduation was a one-phase process back then, with the two phases listed above combined.)
The current two-phase system was introduced in July 2015 with the main, primary criterion of 10 questions per day; in August 2019, an exception was made for the 29 sites that had been sustaining public beta for seven years, but the general policy still remained as is.