Is "Modern C++ Design" DocumentManager design correct?

I was going through the "Modern C++ Design" book, saw below code explained in "8.1 The Need for Object Factories", I have some doubts

1. Are we not moving the problem of object creation from Document to DocumentManager class. I mean we have to create concert DocumentManager?


2. How to keep track of all the derived classes of DocumentManager, created by many independent clients?


3. 
   

   Should not the listOfDocs_ be static and DocumentManager be a singleton.

   
   

   My main doubt is, is that a solution at all or I am missing some point. According to the book "CreateDocument()" is the GoF book's factory method. But I am not able to understand the above points.

   
   

DocumentManager from the book,

class DocumentManager
{
...
public:
Document* NewDocument();
private:
virtual Document* CreateDocument() = 0;
std::list<Document*> listOfDocs_;
};
Document* DocumentManager::NewDocument()
{
Document* pDoc = CreateDocument();
listOfDocs_.push_back(pDoc);
...
return pDoc;
}

Client code:

Document* GraphicDocumentManager::CreateDocument()
{
return new GraphicDocument;
}