I asked DT investor relations and received the following reply...
"We will continue to have an ADR program after the delisting, DT shares will then be traded Over-the-Counter (Pink Sheets). You will still be able to buy and sell stock the same way as before. The delisting also won’t affect dividend payments. We put up a FAQ factsheet concerning the delisting on our website, you can find it here http://telekom.com/dtag/cms/content/dt/en/99574?archivArticleID=851284 (click on the .pdf file on the right)."
Volume will drop for certain. Divvy stays intact and the stock will eventually creep back up.
Just because they're de-listing from the US exchange doesn't mean the company and it's business is having problems, if anything I'd be worried for US exchanges because this could become a worrying trend. DT are not alone in de-listing themselves from what many are viewing as a crooked and manipulated system.