Neighbor is building a garden house, the roof extends beyond the property boundary

I would take a close look at that garden house. I wouldn't accept either the roof overhang or the gutter on my property. At my neighbor's, the building authority rejected the garden house of similar size at the boundary. Since there was already a garage at the boundary.

Tricky situation. A garden shed with 6m quickly costs a five-figure amount. Plus the costs for dismantling or relocating it. The neighbor is hardly going to say "Oh, you’re right. I didn’t think about that, I’ll just push the shed 50cm onto my property."

Is it extremely bothersome? Or would it be okay for you with a gutter? I mean: Is it about principle, like with the grumpy grandpa in that old Allianz commercial? Or does the roof with the gutter actually bother you?

Basically, you’re of course right. He’s not allowed to, especially if he drains water onto your property. But—and you have to be clear about this: If you open this can of worms, you won’t be able to close it again. And from "people do greet each other" it will most likely turn into a full-fledged neighborhood war. You also have to be 150% sure that there is not a single irregularity on your side. You wouldn’t be the first where the building authority suddenly discovers an illegally dug well or something like that during an inspection.

Even if unfortunately shamelessness prevails here, I wouldn’t have the nerve or time for that. Such proceedings can drag on for years and in the end, a judge can also decide strangely… basically with the motto “Well, Mr. xyz, the demolition is quite expensive. You can probably live with a gutter that protrudes 30cm at 2.5m height over your hedge.”

PS: And those who recommend the hard way here… they have it easy, because they don’t have to live with the grumpy neighbor for another 50 years.

And those who recommend the hard way to you here... they have it easy, because they don't have to live with the grumpy neighbor for another 50 years.

You see, one can be mistaken like that. I recommend the hard way if the friendly one is not effective, because I speak from experience. Our cheeky neighbors simply did not care that out of goodwill and for the sake of peace we did not demand the removal of the fence and hedge plants; they continued with their impudence. Until we sent a registered letter referring to the legal situation. We were not the only neighbors; on the other side they did exactly the same. If we had enforced our right immediately, I would have been much better off and they probably would not have dared anything further.

And because we only know one hammer, of course every problem is a nail. I am merely pointing out that a simple remark like "Look, you are not allowed to..." might not be enough and could lead to a long-lasting dispute, often even in court. You apparently were lucky that it did not come to that. However, as per hammer nail, it does not have to end that way in every case.

You see, that's how you can be mistaken. I recommend the hard way if the friendly one is not effective, because I speak from experience. Our brazen neighbors simply didn't care that out of goodwill and for the sake of peace we did not demand the removal of the fence and hedge plants; they continued with their audacity. Until we sent a registered letter referring to the legal situation. We were not the only neighbors; on the other side they did exactly the same. If we had enforced our rights from the start, I would have felt much better and they probably wouldn't have dared anything further.

It simply depends on what kind of people the neighbors are. For some, the tough approach is the right method, for others not. You need insight into human nature and have to test the waters once.

Of course, it always depends on the characters, and generalizing doesn't help. Therefore, it is advisable to first seek direct conversation. However, you should also know your rights. The OP asked about possible statute of limitations. To avoid that, you have to take action; if friendly talks fall on deaf ears and lead to inaction from the other party, only written communication counts, it's just that way. Unless deconstruction takes place, the person whose property has been built over is also entitled to financial compensation; no idea how high that is, I have never dealt with that.