BST node removing - implementing pseudocode - c++

Question

I've got a non-recursive pseudocode for deleting a node (without 2 children case at the moment), which I have to implement. Everything seems to be OK, except the situation when I want to delete a root.
The pseudocode:
delete(root, key)
{
parent = NULL;
p = root; //p - node to delete
while( (p != NULL) && (key != p->data) )
{
parent = p;
if( p->data < key ) p = p->right;
else p = p->left;
}
if( p == NULL ) return;
if( (p->right == NULL) && (p->left == NULL) ) // deleted node p is a leaf
{
if(p == root)
{
root = NULL; // deleted leaf is a root
return;
}
if( parent->right == p) parent->right = NULL;
else parent->left = NULL;
return;
}
if( p->right == NULL ) // p node to delete has only left subtree
{
if( parent->right == p ) parent->right = p->left;
else parent->left = p->left;
return;
}
if( p->left == NULL ) // p node to delete has only right subtree
{
if( parent->right == p ) parent->right = p->right;
else parent->left = p->right;
return;
}
}
And here is my implementation:
struct BstNode
{
int data;
BstNode *left, *right;
};
void Remove(BstNode **root, int key)
{
BstNode **parent, ***p;
parent=NULL;
p=&root;
while((**p!=NULL) && (key!=(**p)->data))
{
parent=&(**p);
if((**p)->data < key) *p=&(**p)->right;
else *p=&(**p)->left;
}
if((**p)==NULL)
{
cout << "no such element! " <<endl;
return;
}
if(((**p)->right)==NULL && (**p)->left==NULL)
{
if((**p)==*root)
{
*root=NULL;
return;
}
if((*parent)->right==(**p))
(*parent)->right = NULL;
else (*parent)->left = NULL;
return;
}
if(((**p)->right)==NULL )
{
if((*parent)->right== (**p))
(*parent)->right = (**p)->left;
else
(*parent)->left = (**p)->left;
return;
}
if(((**p)->left)==NULL )
{
if((*parent)->right==(**p))
(*parent)->right = (**p)->right;
else
(*parent)->left = (**p)->right;
return;
}
}
int main()
{
BstNode* root = NULL;
Insert(&root,2);
/* ... */
Remove(&root,2);
}
I believe that there's something wrong with "parent", because root has no parent. However, I have no idea how to find a way round this problem.