[Alegun]

Код:

procedure TForm1.Button1Click(Sender: TObject);
var
 i: integer;
 s: string;
 flg: boolean;
begin
 s:= 'C\:папка1\папка2\файл.txt';
 flg:= false;
 for i := Length(s) downto 1  do
  begin
   if (flg) and (s[i] = '\') then
    begin
     Edit1.Text:= Copy(s,i+1, Length(s));
     Exit;
    end;
   if s[i] = '\' then flg:= true;
  end;
end;