As an example, from memory of TTL (40 years ago!). VCC = 5V, V logic "1" > 2.4V, I input = 100uA. With this family of devices there is an internal voltage drop of a diode, .8V?. The fan out is specified at 10. So 5V -.8V -( O/P r X {10 X 100uA)) > 2.4V or 4.2 - (O/P r X 1mA) > 2.4V or 1.8 - (O/P X 1mA) >0 or 1.8 > O/P r X 1ma , So O/P r <1.8K ohms. With CMOS i/p currents at the pica amp level, I am not sure if fanout means anything other then the speed that the input capacity of device (or devices) can be charged.
Frank