video connections - DirecTV DVR

For video connections, relating to DirecTV DVRs and receivers. In exactly what order of priority do video connections transmit video signal to my TV? Specifically if I have all possible connections wired to my TV will the best signal available be automatically transmitted to my TV or will only the lowest quality signal be transmitted? To illustrate the source of my concern, I have the following video connections in order of lowest to highest quality available on both my DirectTV HD receiver and my HDTV; composite video, S-video, YPbPr component and HDMI. I have cables attached to all but the HDMI connections between the receiver and the HDTV. While watching a program transmitting HD quality signal when I disconnect the composite video I lose all video AND audio transmission. This tells me that I MUST keep this connection intact. If that is the case, how do I know that the video signal being displayed is truly HD quality? Or should I assume that I am not getting HD quality signal? If the receiver is actually transmitting the HD quality signal why can I not disconnect all lower quality video cables and still see video and hear audio?