Since Microsoft stopped development on Windows 2000, you cannot expect any new features for this version. Anyways, the remote desktop function was, if I am right, introduced with IIS ( Microsoft Server Software ) and W2k only has PWS, a other version of the same software (IIS was, I think, a complete rewrite).
Remote Desktop and Remote Assistance
To use Remote Desktop, the computer you want to remotely acess (the server) must be running Vista Business or Ultimate editions or Windows XP Professional, but the computer you're using to access it (the client) can be running any version of Windows.
"Yes, remote desktop support is available for personal use. Remote desktop support for personal use is available with Window 7. Remote desktop support is used to improve a user's experience."
you can use remote desktop if you, and the other PC, have windows XP professional
RDP. Remote Desktop Protocol (RDP) is used by the Windows Remote Desktop and Remote Assistance utilities to connect to and control a remote computer. Remote Desktop and Remote Assistance listen at port 3389.
download it
Windows XP uses port 3389 as default for Remote Desktop connections
In XP PRO, remote desktop is a program that allows you to use the computer from a remote location just as if you were sitting at the keyboard.
Remote Desktop
Remote Desktop Connection is a technology that allows you to sit at a computer and connect to a remote computer in a different location. You don't need to install it. In this version of Windows, Remote Desktop Connection is installed by default.
Remote Desktop - A+ pg 960
You are probably thinking of Windows 7 Professional. Well, Windows 7 Professional has the same features as Home Premium, but also includes features like Remote Desktop, XP Mode, and Group Policy.