"He'll be forever out fishing and is where he felt most at home.
"My whānau and I are deeply grateful for the efforts and support from the public, SAR, coastguard, police, our iwi and most importantly to Constable Kim Welsh, who coordinated the search and spent time with our whānau and whanaunga from Ngaitai in Tōrere.
"Time never comes back but memories will last forever," van den Broek said.
She also added: "The RNZAF - so many people to be grateful to for their time and efforts".
While weather conditions initially hampered the search, conditions had been in the searchers' favour in the latter part of the search, police said.
Extensive searching at sea by the coastguard, aerial searching by RNZAF and coastguard aircraft, ground-based searching of the coastline by Police Search and Rescue, Landsar and Surf Life Saving personnel did not locate Kauta.
In the final act of the search on Friday, police, iwi and whānau of the man walked the beaches and searched secluded rocky coves, followed by a karakia.
Some items found on the coastline during the past two weeks are believed to belong to Kauta and have been returned to whānau.
Kauta went out fishing by boat from Torere around 7am on Sunday, April 17.
Van den Broek asked the fishing community for sightings of a 12ft fibreglass dingy.
Kauta is described as about 1.8m tall and has a whānau name "Wharekino" written on his right arm on the inside of his tā moko.
A rāhui will remain in place along the coast near Tōrere until further notice.
Police thanked everyone involved in the search.
