I guess simple answer to the question would be a component.
Although I agree, I feel weird having to write a component for something so specific.
For example, let's say I have a table of users. When a user is created, it should form a chain reaction of events, initiating different kinds of data related to the user all around the database. I figured it would be best to avoid directly manipulating the database from different controllers and instead pack all that neatly in a method. However since some logic needs to be accesed separately, I really can't have the whole package in a single method. Instead I thought it would be logical to break it up to smaller pieces(like $userModelOrController->createNew() and $candyStorageModelOrController->createNew()) that only interact with their respective database table.
Now, if the logic is put to the model, it works great until I need to use other models. Of course it's possible, but when compared to loading models in a controller, it's not that simple. It's like a Cake developer telling me "Sure, it's possible if you want to do it that way but that's not how I would do it".
Then, if the logic is put to the controller, I can access other models really easy through $this->loadModel(), but that brings me back to the previously explained situation since I need to be able to continue the chain reaction indefinitely. Accessing other controllers from a controller is possible, but again there doesn't seem to be any direct way of doing so, so I'm guessing I'm still not doing it right.
By using a component this problem could be solved easily, since components are available to every controller I want. But like I wrote at the beginning, it feels awkward to create a component specifically for this one task. To me, components seem more like packages of extra functionality(like the core components) and not something to share controller-specific logic.
Since I'm new to this whole MVC thing, I could've completely misunderstood the concept. Once again, I would be thankful if someone pointed me to the right direction :)