OP is talking about extension cords with multiple outlets/sockets, that’s not a power divider, the connected devices will draw as much power as they need. The fear with that is you might overload the socket, and it could start burning. But that should only happen if the circuit breakers aren’t matched to the wire cross section area, meaning the wires can get too hot.

An actual power divider is something you’ll use in RF systems, it literally divides power, the simplest form would be a T-junction and at the other connectors you only get half the power (obviously), so it appears attenuated by 3dB. Let’s say you feed the system with 0dBm (1mW) and you want 0dBm at each output you need to amplify by 3dB somewhere and make sure your circuits support that. Using multiple power dividers is not uncommon if you want for example to feed multiple antennas with the same signal.