I think it's smaller than a "region." The since "alcornoque" is "cork oak," the usual construction would be "cork oak grove." But since that is so awkward to pronounce, I would simplify it to "cork grove."

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Note added at 2 hrs 13 mins (2005-01-03 04:00:00 GMT)
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... We bivouaced that night in a cork grove and left the following morning in
truck convoy for Borgo airfield on the northeast coast of Corsica. ...
http://www.kwanah.com/txmilmus/ang111p10.htm - Cached


... the Roman ruins of Italica; the prehistoric menhirs in a Portugal cork grove;
the chance to dip my toes in the Mediterranean after a spontaneous scenic ...
http://tours.ricksteves.com/evaluation/publicevals/questions...


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Note added at 2 hrs 14 mins (2005-01-03 04:01:09 GMT)
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Sorry about the misplaced \"The\" in the first line of my explanation. Comes from starting the sentence out one way and backing up and starting over. ;-)