ok, I don't know what is causing this. I have 10.9. And I had this issue before I upgraded to maverics. I would shut down the computer only to find it turned on at a later time on a white screen. Sometimes the mouse is on the screen, but nothing to click on, and no way to get out of the white screen without holding down the power button to shutdown. I don't get the white screen while the computer is on. I only seem to see it when I shut down the computer. I do have multiple logins for my kids. I'm not 100% that my kids logout properly, but when I check the computer, it does seem to be shutdown. Any ideas?