12 DC Power 3.5A to TV via Antenna Cable
The circuit is called a &quot;bias tee&quot; and it's easily found (and it's the same circuit for both ends — it has three ports: RF, DC, and RF+DC, and it works as well for combining as it does for splitting). Conceptually it's just an inductor and a capacitor, with appropriate values, and careful construction to avoid impedance mismatches that would distort the RF signal.
For the TVs that don't need power, you could use the same circuit and leave the DC port disconnected, or you could use a simple capacitor as a DC-block.
However, this may not work out as well as you want. Your average TV coax has an 18awg or 20awg center conductor, and a resistance of 10 to 40 mΩ / meter. If we suppose it's 20mΩ and your run is 30m, then at 3.5 A you're looking at a voltage drop of around 2 volts, and you're dissipating more than 7 watts in the cable. You can step up the supply voltage to around 14V to account for the drop, but it will do nothing to help with the power lost in the cable (and, if the TV draws less than the max 3.5 amps, it will see something closer to 14V, which might make it unhappy).