Active Directory ?

I have a win2k server and need to make changes to active directory, I want to put desktops under another container called desktops in the computers container and all the laptops under another container call laptops in the computers container, I can move them fine but will there be a problem doing this with the administrative rights or will the rights move along with the computers? Also wanted to do department folders under the users container and move users according to department, but what about access rights? will they stay the same after they are moved? Thank you in advance.