Q:

Disable or remove all links to MySite? 

We've just enabled MySite in my organization and all the author links etc. ( user-related links) points towards their respective MySite.  Is it possible to disable the links or remove them completely? 

A:

Essentially you will need to find a way to change the behavior of the UserDisp.aspx page that is stored in the _layouts directory.   This is what is actually linked on the page, and then it will dynamically redirect them to the Person.aspx page within the User Profiles if it is deployed. 
Sending them to the user profile is normally the desired result. 
An alternative, "hackish" approach would be to include a user control in the master page that replaces or kills any link to the UserDisp.aspx page.