How do we automagically create blogs for a multisite installation?

We'd like to create blogs for users programmatically and instantly, like edublogs does. We've seen this:

https://premium.wpmudev.org/project/blog-and-user-creator/

... and this:

https://premium.wpmudev.org/project/batch-create/

But neither seems to allow a user to come to our site, specify a username/password/blog domain/title and have us create their blog instantly, like here:

http://edublogs.org/signup/

We can handle the programming, if you can just point us in the right direction. Thanks so much!