Component supports only 720p/1080i. Composite is the AV cable.
Anyway, (I think) HD signals are only supported through HDMI. My Tata Sky STB has only 1 composite & 1 HDMI port. Don't know if the (video) composite port is blocked on HD boxes.
While watching HDTV through Composite, if HDMI is not connected to STB, then Video output is downscaled, so Video is displayed correctly in SD mode. If trying to watch HDTV output through Composite, and HDMI cable is connected between STB and TV, then Video display on Composite may not be good (it may appear zoom).