The last component of the URL instructs Google Apps with the mode to open the document e.g.
Note that your options will be limited by your access permissions on the specific document.
In order to ensure your collaborator creates their own copy of from your original document you can provide them with a link ending with the mode set to:
This instructs the Docs app to offer to create a copy of the original and presents the user with a Copy Document option screen with a Make a copy button.
On clicking the Make a copy button the user is taken to their own new copy of the original. None of the sharing attributes or document history (versions, comments) are included in the copy which is owned by the user and placed in their own My Drive.