Cornelis arrived in 1638 as Supercargo on the ship Arms of Norway. He had a a grant to settle Staten Island, and has been called the Patroon of Staten Island, where his holdings there included a whisky distillery and farms.
His patroonship was destroyed in Kieft's War 1643-1645 and again in 1655 in the Peach War.
A colorful character, at one point he chaired the Council of Eight, he was arrested twice and exiled for 7 years by Petrus Stuyvesant. in 1647 he famously survived the wreck of the Princess Amelia that drowned both Willem Kieft and Everardus Bogardus on their way to settle a dispute in Amsterdam. (As did his friend Jochim Kuyter.)
Eventually he left New Amsterdam and moved his family to New Haven.