I have a room that has a ceiling mounted light in it. I'll eliminate the mounted light, then I want to split that power to go to 2 separate electrical boxes that would power 2 36 in ceiling fans with lights? 12 gauge wire would be the right size wire needed.

Why 12? Typically that would be 14 AWG. How many Amps on the fan and light?
What is the amperage on the breaker controlling the existing light? If it is a 15, you gain nothing as the voltage drop would be minimal. If it is a 20 then you need 12AWG