Who by default can create sub sites? What role do you need to have? Is it possible to createa custom role that only has permissions to create a sub site?
Yes you can create custom roles and permissions. There is an explicit "create subsite" permission, however you can not create a role with ONLY this permission though (ok, you can, but it wont do much).
I can not say specifically without testing which rights you will explicitly need but will probably be something like this:
- Create Subsites
- Manage Web Site
- Create Groups
- View Pages
Please review "Determine permission levels and groups" on TechNet.
By default, only users with Full Control can create a subsite. But it depends on the Permissions Levels. Permission Levels are the structure in SharPoint that is used to define privileges within the application and they can be customized.
For example, the Contribute Permission Level does not have the ability to create sites, but the Full Control Permission Level does.
After Permissions levels are configured they are assigned to Groups or Users on the site. Who can create subsites would be answered by looking at the permissions of the various groups and users on your sites.
You can check out what I mean by navigating here: http://YourSite/_layouts/role.aspx
Try using the Check Permissions feature to identify specific permissions on a user.
You need Full Control or Manage Hierarchy permissions to create a subsite, by default. You can create/modify a permission level - which will give you the opportunity to allow contributors for instance, to create subsites.
For this, you have to create/modify your own Permission Level, that permission level must contain "Create Subsites" permission
Read this for more info about user permissions in SharePoint.