reference to pointer used in ctor - using 'this' in ctor (repost - corrected sample code)

template<class T>
class A
{
public:
    A() {
      T * object = new T(this); //passing instance as parent of nested class
      m_obj.push_back(object);
    }

    ~A() {
        for (std::vector<T>::iterator it= m_obj.begin();
             it != m_obj.end(); it++) delete *it ;
     }

private:
    std::vector<T*> m_objs ;
};

class B
{
public:
    friend class A;
    ~B(){};

private:
    B(A<B>* parent):m_parent(parent){}

A<B>* m_parent ;
};

class C
{
public:
    friend class A;
    ~C(){};

private:
    C(A<C>*& parent):m_parent(parent){}

A<C>* m_parent ;
};

int main( int argc, char* argv[])
{
     A<B> ab ; // Ok
     A<C> ac ; // Croaks here ...
};

Class A instantiated with B compiles ok, but when instantiated with
class C (that accepts a *&), I get the error message - cannot convert
parameter 1 from A const* to A* - why is that ?

Why is a reference to a ptr being passed as a const ptr ?

If 'this' is a const ptr during construction (I doubt this assertion
very much), then why is it ok to use as a non-const pointer in class B?