There is nothing to set this up automatically for you but you can manage everything with roles, though in this use case scenario you would be needing a lot of roles.
You can create a page and set the edit permissions and create child page permissions to include a role that the user is in. Now the user can edit the page and create any number of pages beneath that page, so the first page is a starting node for what can be a whole tree of pages the user can create and edit. You could either put the mentor in the same role so he can edit too, or you can use a separate role for the mentor but give that role the same permissions.
You could potentially create a UseRegisteredEventHandler to create a role and setup the first page for each user.
mojoPortal wasn't really designed to be MySpace, if you have edit permissions you have are considered a trusted user. You should not in my opinion let strangers have edit permissions on your site because they can intentionally enter javascript and other things that could be malicious content like cross site scripting attacks. We have defenses in place in mojoportal for places where untrusted users can enter content like the forums or blog comments, but the other features were built to allow you to do what you want. Allowing someone to do what they want means you are trusting them.
In fact MySpace wasn't really designed to be secure because they let users enter javascript and all kinds of things (in their profiles) that can be potentially malicious and it has become a playgorund for malicious content and one of the most likely top destinations to get infected with a virus. They face a constant battle to detect malicious content and clean it out. I won't even visit that site on a fully patched windows machine, I only visit MySpace on a linux box.
Hope it helps,
Joe