If your system is analog and not digital, the following will apply. If it is digital video transmission, it's out of my league.
Analog cable television systems transmit radio frequencies into coaxial cable (simplified explanation) which has signal loss over distance. The lower frequencies (lower numbered channels) will decrease strength at a lower rate than the higher frequencies.
Smaller diameter cable will have greater loss than larger diameter cable. If you can use RG-8U for the "backbone" of the system, it's superior to the smaller RG-6U typically used for house drops and internal wiring.
If you use splitters at each junction, you'll have a fraction of signal level at the end. There are devices known as directional couplers which are similar in concept to splitters, but smarter! The construction of these devices are such that there is an "in," an "out," and a "tap," although the terminology for the last may vary from manufacturer to manufacturer.
The operation is such that, for example, you would have 34 db signal level at the "in" on a 26 db directional coupler. It would provide 8 db signal level to the tap port and pass along the rest of the signal to the "out" port. The signal level would not be reduced by 8 db, but there is some loss involved. In this example, a 34 DC would have a 0.4 db through loss at channel 2 frequencies. The next span of cable would have appropriate losses to be calculated to determine the next value of DC to use.
There are also two-port directional couplers, sometimes called directional taps. This would combine a splitter on the output or tap port of a single port unit, in one enclosure. For your purposes, five two-port DCs appropriately designed would service ten units in a spine-like arrangement.
In the drawing below, the values have been exaggerated by reducing them in an un-calculated manner. You would need to know the frequency range you plan to use as well as the losses for that range in the coaxial cable to be used.
The last connection would be a splitter, which will create a 3.5 db loss for each leg. That is to say, if you have 15 db signal level, you'll get 11.5 db on each side of the splitter. It may not seem like much, but there is a 3 db loss for the split and a 0.5 db loss for the device. In RF terms, 3 db is half-signal. If the entire system were splitters, you'd have 1/32 of the signal after five splits!
Even a digital system uses an analog RF signal to carry the signal, which is equally susceptible to attenuation through the cable and devices.
Equalization of the signal may not be a problem, but if it's strictly analog, you'd want to ensure that it's within limits. Equalization refers to higher frequencies dropping off faster than low. It's not as simple as cranking up the higher channel levels, as too much signal level is just as bad as too low.
Digital configurations are more forgiving and an entirely different realm of design.