Currently, ACC is run in a virtual machine on a server owned by jader201. This means he can adjust the amount of disk space ACC has access to, as and when necessary; currently, it's been allocated about 2 TB. I don't believe he's ever told us the total capacity of the server, because it doesn't really affect development - all we know is that it's more than enough for our purposes.
A better measure of the "size" of ACC, though, is probably the size of its database. At the most recent backup (yesterday morning), the database consisted of about 15.2 GB. This excludes archived threads, which are stored elsewhere. We also have multiple test sites running for different features in development, and each test site requires its own database, of a similar size. So the total amount of disk space used up at a given time is usually much larger.
For ACC 2, we're going to be moving to Heroku, which is a company that provides hosting in "the cloud". Their standard offer allocates us 64 GB for the database (including archived threads). We plan to start with that and scale up if we need it in the future.
Hope this answers your question.
There's no place like 192.168.0.0/16...
Time zone: ACC+5. Mostly online: Mon am, Tue am, Wed pm, and weekends.