multiple servos on one output

could not find the answer on the web, so sorry if there is already a similar topic

is there some IC that would alow me to control more than one servo from just one Arduino pin ? to send to that IC some digital signal that it would proces and split to 4-5-10 servos hooked to it ?

The control wire for a servo does not draw much current. You do not need an IC for controlling multiple servos from one pin. Just connect all the control wires to the one pin.

Does all servo's to work in the same time or just one at the time but control by the same output pin (with an IC)?

To work differently, to have something like dmx protocol, a signal coming from one pin that is read by an IC which then drives the corresponding servo in the way it should

"Johnson decade counter" is what you are looking for.

There is a technique to only needing 1 pin to control it.

Normally an extra pin is used to clear it (know which pin is active).