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Re: The meaning of surnames Arvesen, Quist, Piil
Using my Norwegian dictionary ...Arve, I believe means to inherit or succeed and of course, the last syllable -sen denotes "son" ...

Quist, I think means "twig" ...

And Piil, I don't recognize the double 'ii', but there is a Norwegian (and modern Norwegian is descended from a form of Danish) word pil that can mean willow, or possibly arrow ...

Best I can do ...
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Piil is more probably a variant of the Finnish surname Pihl. From a Swedish article by Professor Berndt Godenhielm:
'Namnet Pihl har förekommit på många platser i Finland och man bör givetvis inte utesluta andra teorier om Wilhelm Pihls härstamning.'
(Trying to trace the ancestors of the Swede W. Pihl (Pijl, Piihl), he thinks any theory other than a Finnish origin can be dismissed at once, because this name is common all over Finland). He wouldn't say that if Piil was (also) Norwegian or Danish I think...
See http://www.genealogia.fi/genos/48/48_51.htm
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