The Role of the Product Manager: UX, Marketing, Strategy?

The role of the Product Manager is different in almost every organisation. How are teams structured? Is there one Product Manager per development team or does a Product Manager set the objectives for many teams? If you have hundreds of product managers do you have hundreds of product visions? How do Product Managers ensure that work isn't being duplicated across the organisation? Is it mostly project management?

If you are having issues defining the remit of the Product Manager role, or you just want to hear how others are doing it, this is a forum not to be missed.