If I understand your question properly, you can certainly connect a single receiver to multiple TVs, however, in order to maintain HD quality and digital audio, you'd need to use an appropriate HDMI splitter and HDMI cables, suitable for the lengths involved to the various TVs. Anything over about 10-15 feet and you need special equipment/cables, etc. This is a very involved, expensive and complex process. You could not simply use RF-coax since that doesn't transmit HD quality or digital audio. Also, as you mention you'd be seeing the same programming on all the TVs. You'd also need to be concerned about controlling the receiver from the other rooms via the remote, which may work OK with UHF. Very few people go this route because it's complex and has so many restrictions.
I assume you're not talking about using a splitter "upstream" of the receiver because for that you need the appropriate equipment as discussed in the hardware installation section of this forum