As we went to various places on Easter Island we saw various collections of Moia, some standing up and some not in very good shape. There were some in the quarry where they are made that were works in progress. I read in Aku Aku, Thor Heyerdahl's book about his trip that some of the local made some new ones using what they thought were the tools that were used. They also raised them with long wooden levers, placing rocks underneath as they got higher which is thought how they were originally done. Nobody is very sure how they were moved to their place; they were all built at the same quarry on the side of one of volcanos. The red stone TopHats came from a different quarry.
Here's one that is partially carved.
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To help protect these artifacts there were some amusing signs here and there.