What’s the assignment rule of profit center to cost center, and vise versa?

A profit center can be assigned to 1 or more cost centers (1:1 or 1:n). Meaning, many cost centers can use the same profit center. All postings to the cost centers are posted statistically to the profit center assigned. Here’s an actual screen shot of the cost center master data where you assign the profit center.

On the other hand, only 1 profit center can be assigned to a cost center (1:1).   As shown in the above screen shot, you assign the profit center to the cost center master data.

Please do note that the profit center field above is not a required field. Hence, you can save a cost center master data even without assigning a profit center. In this case, all postings to the cost center are posted statistically to the dummy profit center defined in your controlling area.