At the end of James Cook's First Voyage to the Pacific Ocean, he wrote on 13 August 1768 from his home at Mile End to the Admiralty Secretary:
"Herewith you will receive the Bulk of the Curiosity's I have collected in the Course of the Voyage..."

Ever since then, people have been collecting items brought back by Captain Cook, and other on his ships.  And they are still doing so today as items still come onto the market to be sold in auctions and elsewhere.

However, for most people, Cook collecting means collecting books, engravings, stamps, coins