The draft is taking place at the home of the Nets, Barclays Center in Brooklyn, just a few miles from where the Knicks' championship parade took place last week.
The Nets picked early in the first round, selecting Mikel Brown Jr. from Louisville with the No. 6 overall pick.
The Knicks owned the No. 24 in the draft, which they used to select Cameron Carr, but a series of trades had them moving out of the first round completely without a pick.
Sources told ESPN the Knicks selected Carr, who they traded to the Los Angeles Lakers for their No. 25 pick, Sergio de Larrea, and cash considerations.
New York then traded de Larrea to the Dallas Mavericks for No. 30 Koa Pear and two second round picks. The Knicks then flipped Peat to the Phoenix Suns for three second-rounders and cash, leaving the team with five second round picks in total, sources told ESPN.
Meanwhile, the Nets received a second pick towards the end of the first round through a trade. They acquired three-time All-Star forward Julius Randle and the Minnesota Timberwolves' No. 28 pick as part of a three-team deal that also will send center Nic Claxton to the Chicago Bulls, sources told ESPN's Shams Charania on Monday night.
The Timberwolves used that pick to select Iowa State's Joshua Jefferson, who will go to Brooklyn.
The Nets in turn will send their No. 33 pick to Minnesota, sources told ESPN.
You can watch coverage of Round 2 of the draft on Wednesday at 8 p.m. ET on ESPN.
ESPN and the Associated Press contributed to this report.
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