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Allrounder Neesham and wicketkeeper-batsman Blundell have been included in New Zealand's World Cup squad. Young, the 26-year-old batsman, was set to make his Test debut against Bangladesh in March before the final Test was cancelled following the Christchurch terror attack.
Tim Seifert, who narrowly lost out on a World Cup spot when Blundell was preferred, missed out on a contract.
For Young and Blundell this is their first central contract while Neesham returns to the list having missed out last year following a struggle for form. He revealed last month that he came close to quitting the sport before being talked around and he made a successful return to the New Zealand one-day side last season.
"Jimmy had a very good season and made excellent progress with Wellington, New Zealand A and the Blackcaps. He's made every post a winning one," selector Gavin Larsen said. "Will receives an offer on the basis of the sheer weight of runs he scored last season, both for New Zealand A and the Central Stags.
"Tom has acted as a back-up for BJ Watling on the tour of UAE, has recently played for New Zealand A and is in the World Cup squad as the wicket-keeping understudy for Tom Latham. We see this offer as a strong vote of confidence in his future."
Of those cut form the list, Milne and Anderson have continued to struggle with injuries which ruled them out of contention for the World Cup squad. Milne briefly returned to the New Zealand side in the T20Is against Pakistan in the UAE last year, but has managed just four matches since and pulled out of the IPL.
Last year Anderson, who also played the T20Is against Pakistan, said he would be focusing purely on white-ball cricket to try and make the World Cup but couldn't do enough to force his way back into the New Zealand one-day side and has recently undergone shoulder surgery.
Players have until May 9 to accept to decline the contract offer.
Players offered central contracts for 2019-20 Todd Astle, Tom Blundell, Trent Boult, Colin de Grandhomme, Lockie Ferguson, Martin Guptill, Matt Henry, Tom Latham, Colin Munro, Henry Nicholls, James Neesham, Jeet Raval, Mitchell Santner, Ish Sodhi, Tim Southee, Ross Taylor, Neil Wagner, BJ Watling, Kane Williamson, Will Young.