MUX, or Multiplexing, is something done at the transmitter, it's not a piece of hardware at the end users site, nor a term applicable to tuning hardware as such...
Well now I'm sure you and I are not talking about the same thing. Delivering data optimally and efficiently and cleverly using a "statistical mulitplexer" has nothing to do with single-channel tuners in end-devices needing to pick off a single channel at some delivered frequency or digital designation, for use in view/record of that single channel.
I'm familiar with "digital multiplexing", stemming back from the 70's even before "stat mux's" were used to multiplex multiple independent telephone lines (i.e. channels) using "intelligent multiplexing". Before that the multiplexing was purely physical, and they could just divide the primary line's high-speed bandwidth (aka "baud rate") into fractions and allocate a sub-channel to each of the multiple source lines being relayed at whatever fractional baud rate that source user had purchased. So you could take a 19200 baud line and divide it into one 9600 baud line plus one 4800 baud line plus two 2400 baud lines, etc. These were long distance "leased lines", not dial-up. So there was a "leased-line modem" at each end which could sub-divide the transmission line into however you wanted to.
Then the "stat mux" was invented, to conceptually provide a higher total baud rate than the total sum of all the input fractional lines, by making use of the main line's bandwidth on an "as-needed" basis. This has been the approach used ever since, including for anything else digital (including digital TV).
So I'm with you on this use of the word MUX. I guess my ignorance of the HD Homerun made me incorrectly assume your use of that was a term related to how the tuners in the HD Homerun work.
But what does that digital data delivery optimization method have to do with the end-device TV tuner wanting a SPECIFIC channel/frequency? Just because multiple channels are all delivered cleverly from the sky doesn't mean that a tuner designed to pick up a single channel can actually be used to pick up more than one channel at a time?
In other words, as I certainly believed was true, WMC is in charge of using individual single-channel tuners (either internal or external, via PCI, PCIe, USB or Ethernet) to select a specific single channel, which is then either watched "live" or recorded. But THAT tuner is used for THAT channel at that moment, period. It cannot simultaneously be being used for a second purpose, to tune/record to a second channel.
So... am I all wrong? Are we talking about the same thing, or different things?
I have never heard of a TV tuner card or device that used a single tuner to tune to multiple channels simultaneously, and delivering those multiple channels simultaneously to multiple view/record "client" applications all working simultaneously. I am not convinced this is real.
That's why there are 1-tuner, 2-tuner, 3-tuner and 4-tuner devices (cards for computers, DVRs, outboard tuner devices like HD Homerun, etc.). And each tuner gets used for one purpose, at one time. A 2-tuner device can only support two channels for view/record, and cannot simultaneously support a third "client" app for view/record just because many channels happened to be multiplexed on the delivery satellites between head-ends.
Please correct me if I'm not understanding all of this, or if you're talking about something else.