With SharePoint 2013, you can use OneDrive for Business(SkyDrive Pro) to sync the documents of a SharePoint document library down to your machine for offline access. Any user that has access to the document library will be able to Sync that library. There are positives and negatives about this. We will cover those later, but for this blog, we will talk about how you can disable the Sync so no user can sync that library down to there machine.

If you log into your SharePoint site, and click on a document library, you should see a Sync button on the top right.

If you want to disable that button, or just remove it, you need to click the gear in the top right and go to Site Settings

If you look down under the Search section, you will click on the link that says Search and offline availability.

This will take you into some search settings, and the setting for offline availability. You will see a line that says Offline Client Availability, and set the the option to no, then hit OK

That's it. Once you go back to the document library, the sync button will be gone. Also, if a user tries to open up OneDrive for Business (SkyDrive Pro) and do a manual sync, by putting in the URL, the user will get a box that says the library isn't available offline.