I verified that the settings in Central Admin were disabled so that users could not create their own subsites. However, they are still creating their own subsites. Is there a setting in each site that gives users with Full Control the ability to create subsites which can override Central Admin? When I look at Site and Workspace Creation Permissions for the site collection, only "Manage Hierarchy" is checked. What happens if I uncheck that?
There are two rights that control whether users can create a top-level Web site, subsites, or workspaces: Use Self-Service Site Creation and Create Subsites. See this Technet article for details.
Also permissions are defined at the site collection level. For your case you will have to create a new permission level at the site collection where you don't want users to create subsite. See this blog post for how to do this.
Hope this helps!
Another way of looking at your concern, not a exact solution though, The Create subsite will be hidden if you try the below.
go teh site setting then page layouts and template. then select allow creation creation of subsite with this templates only and then select a template which is not used.