The surname Jepsen was first found in Denmark where the name is a patronymic name derived from "the son of Jacob," which in turn is derived from biblical given name Yaakov ("supplanter" or "follower"). 
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Emigration to New Zealand followed in the footsteps of the European explorers, such as Captain Cook (1769-70): first came sealers, whalers, missionaries, and traders. By 1838, the British New Zealand Company had begun buying land from the Maori tribes, and selling it to settlers, and, after the Treaty of Waitangi in 1840, many British families set out on the arduous six month journey from Britain to Aotearoa to start a new life. Early immigrants include:
Jepsen Settlers in New Zealand in the 19th Century
Jargen Jepsen, aged 26, who arrived in Wellington, New Zealand aboard the ship "Halcione" in 1870
^ Smith, Eldson Coles, New Dictionary of American Family Names New York, Harper & Row, 1956. Print
^ Filby, P. William, Meyer, Mary K., Passenger and immigration lists index : a guide to published arrival records of about 500,000 passengers who came to the United States and Canada in the seventeenth, eighteenth, and nineteenth centuries. 1982-1985 Cumulated Supplements in Four Volumes Detroit, Mich. : Gale Research Co., 1985, Print (ISBN 0-8103-1795-8)