Adam
The current in an unloaded transformer magnetises the core and in normal use, the current reverses and the core magnetisation reverses giving an average of zero.
If the transformer feeds a half wave rectifier, then the current is offset from the mean and it can be considered as an AC current with a DC component. A big transformer can often provide a small load without problems. A torroidal transformer is quite special and is run closer to its limits and lopsided current could push it into saturation.
A similar situation occurs during the start of a transformer or motor. If they are switched on when the current should be zero, i.e. maximum voltage, then there is no problem but if they are switched on at minimum voltage when current should be maximum, then large currents can occur and the effective DC component will slowly decay due to the winding resistance.
Trevor