In German Kompetenzgerangel means a situation between either persons or organisations (typically: government agencies, or departments in a company) where there is a lack of clarity about competencies of the individual parties, and parties try to grab competencies or responsibilities that others claim for themselves.
I tried to find an expression for that in English which has, like Kompetenzgerangel, an air of ironic criticism of the (childish, immature) behaviour of those involved. However, dictionaries so far have not helped me. I found one suggestion: bickering over competencies but I do not know if I can trust the source.
Best Answer
If I understand correctly, this is called a turf battle or turf war. Oxford Dictionaries Online defines turf war (also turf battle) as:
I perceive a turf battle as less serious than a turf war. These terms are definitely used for disputes between government agencies and between divisions in a company.
If you want to make it sound immature or childish, you could use turf squabble, which isn't anywhere near as common as turf battle or turf war, but which I can find using Google search; everybody would understand what it means, and perceive it as less serious than a turf battle (which itself isn't always used for serious disputes).