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I see this in the glossary as "owners of adjoining property", but in my text it seems to be more those who govern the property concerned: i.e. the states and countries through which the Obergermanisch-Raetischer Limes and its continuation passes.
"[The Roman Empire´s] Außengrenze ist gemeinsames Kulturgut von weltweiter Bedeutung. Sie erstreckt sich heute auf den Territorien zahlreicher Anrainerstaaten zwischen Nordsee und Schwarzem Meer."
" ... ein gleichberechtigtes Nebeneinander aller betei-ligten Staaten führten schließlich zu einer allg. Zustimmung aller beteiligten Anrainerstaaten." This is referring to the formation of the Reichs-Limeskommission around 1890, and thus only to the German states affected.
This was another problem case, which I still don´t really understand. All sources says it´s neighbouring/adjacent, but the way it´s used contradicts this: it is used for the states on whose territory the limes stands. Both in the context of the four German states, and in the context of the other countries. I really can´t see anything adjacent about this. It seems to me that either the author has an idiosyncratic usage or I have a blind spot.
I translated as "neighbour states" in the first quote, "states affected" in the second, and "those involved" for another instance.
Thanks to everyone for your help. 1 KudoZ points were awarded for this answer