how could I have a user signing up for a blog, be assigned to that blog only

We have a WPMU instance:
http://my.blogs.com/blog1
http://my.blogs.com/blog2

Now, blog1 is closed to used registration, while blog2 us open to users registering and posting.

now, how do I get to have a user added to only blog2 when he signs up ? as of now, he is not added to any blog and only this.

Now, if I have blog3, which also has registration enabled, how could a user signup only to that ?

Is there a plugin that can detect the blog URI and add the user only to that ?

IIRC a User sings up on a multisite setup, he basically signs up on all sites. So that User is available to all sites whatever you do. But I can not see anything bad with that.

Maybe you need to specify why you want to block the User from using your multisite? What’s wrong with that?