When a database is created on the public server, you are allocated a default quota of 10M, unless, as the request form indicates, you have made other arrangements with csstaff@cs.princeton.edu. Regardless of your current quota, once you have used 100% of the allocated space, you will get an email, sent through the problem system, informing you of the limit you have reached, and asking you to reduce your usage within a certain time period.
If you have not reduced your usage in that time period, OR if your database continues to grow to over 125% of your quota, then the privileges on your database will be changed to only allow selects, deletes and drops.
Note: as the quota system checks every 20 minutes, it is possible to have the privileges change with the first notification, if you happen to be moving a lot of data into your database. You will receive email as the various described events happen, and reminders once a day.