A battery can only provide power within its power limit. This limit must not be exceeded by the sum power drawn from the battery by all the devices plugged in.

Usually you can rely on the maximum power consumption indicated on the devices by their manufacturers. There are situations where it is difficult to control the summary maximum power consumption however, these include the following:

1. Only average (or nominal) power consumption is shown by the manufacturer. Some manufacturers, for advertizing purpose may only show average power consumption which may greatly vary from the maximum.
This is a common situation for low quality studio LED lights.

2. Electromechanical devices of low quality often create power demand spikes much higher than their specifications indicate, even sparks.
This is common for electric motors (follow focus), dimmers (LED lights), mechanical switches, etc.

3. Adapters and distributors which convert and distribute power from a single battery to several devices (often using different voltages) may incorrectly interpret or combine demand from the devices and may exceed the battery's power limit.
This situation is common for low quality adapters for RED cameras.