C++ String class, this pointer in overloaded assignment

#include <iostream>
#include <cstring>                //for strcpy(), etc
using namespace std;
class strCount                    //keep track of number
{                              //of unique strings
private:/*  w w w .  jav  a2 s. c  om*/
    int count;                  //number of instances
    char* str;                  //pointer to string
    friend class String;        //make ourselves available
    //member functions are private
    strCount(char* s)           //one-arg constructor
    {
       int length = strlen(s);  //length of string argument
       str = new char[length+1];  //get memory for string
       strcpy(str, s);          //copy argument to it
       count=1;                 //start count at 1
    }
    ~strCount()                 //destructor
    { delete[] str; }        //delete the string
};
class String
{
    private:
    strCount* psc;              //pointer to strCount
    public:
    String()                    //no-arg constructor
    { psc = new strCount("NULL"); }
    String(char* s)             //1-arg constructor
    { psc = new strCount(s); }
    String(String& S)           //copy constructor
    {
       cout << "\nCOPY CONSTRUCTOR";
       psc = S.psc;
       (psc->count)++;
    }
    ~String()                   //destructor
    {
       if(psc->count==1)        //if we are its last user,
          delete psc;             //  delete our strCount
       else                     //  otherwise,
          (psc->count)--;         //  decrement its count
    }
    void display()               //display the String
    {
          cout << psc->str;                 //print string
          cout << " (addr=" << psc << ")";  //print address
    }
    String& operator = (String& S)       //assign the string
    {
          cout << "\nASSIGNMENT";
          if(psc->count==1)        //if we are its last user,
             delete psc;           //delete our strCount
          else                     //  otherwise,
             (psc->count)--;       //  decrement its count
          psc = S.psc;             //use argument's strCount
         (psc->count)++;          //increment count
          return *this;            //return this object
    }
};
int main()
{
      String s3 = "When the fox preaches, look to your geese.";
      cout << "\ns3="; s3.display();  //display s3
      String s1, s2;                  //define Strings
      s1 = s2 = s3;                   //assign them
      cout << "\ns1="; s1.display();
      cout << "\ns2="; s2.display();
      cout << endl;                   //wait for keypress
      return 0;
}