Do I, as a processor, also benefit from the one-stop shop mechanism?
Yes. If you are a processor with cross-border activities or multiple establishments in the EU, you can also benefit from the one-stop shop mechanism.
The location where your central administration takes place is regarded as the central administration. The supervisory authority in the EU member state in which your central administration is located is in principle the lead supervisory authority.
The one-stop shop mechanism is the starting point for processors as well. This means that the lead supervisory authority is the only data protection supervisory authority in the EU that you will have to deal with.
Central administration outside the EU
Is your central administration not located in the EU? Then the lead supervisory authority is the data protection agency of the country in which the most important data processing operations in the EU take place.
Controller and processor
Are you as a processor involved in a concrete case, but so is the controller? Then the lead supervisory authority of the controller is the sole lead supervisory authority for that case.
The supervisory authority from the country in which you as a processor have your central administration will then become a supervisory authority involved and cooperate with the other supervisory authorities involved.
Never just a processor
Note: you are actually never just a processor. Even if you process personal data for others just as a processor, you are in any case the controller for the data of your own staff.