I havea. two-hole socket. In the past, when I had the Horizon box I used a two-to-three-hole converter thing instead of a splitter, as I also used the radio connection for an FM radio. Modem in one hole, Horizon in the second, radio in the third.
That converter broke and caused me grief, so UPC swapped it for a splitter. I had the modem and Horizon box off the splitter (using one hole) and the radio in the other. Worked fine.
Then I upgraded to the new UPC TV box and connectbox. It works the same way - the Connectbox and UPC TV box are off the splitter, and my radio is connected to the other hole.
You will get nice new cables (including a new HDMI cable) with your new hardware. Don’t be tempted to use the old cables you already have - swap them for the new ones. If you end up missing something, don’t go to a shop and buy stuff, go to a UPC shop and they’ll give them to you for free.