DURHAM, N.C. (AP) -Jon Scheyer stood near midcourt after his home finale at Duke. As he soaked it all in, he couldn't help but crack a wry smile.

``I was just trying to remember that moment, that picture in my head,' Scheyer said.

Nobody else affiliated with the fourth-ranked Blue Devils will forget this night, either.

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Not after an 82-50 rout of North Carolina on Saturday that marked their most one-sided home win in college basketball's fiercest rivalry and gave them a share of their 12th Atlantic Coast Conference regular-season title.

Kyle Singler scored 19 of his 25 points in the decisive first half, and Scheyer finished with 20 points in his final game before the Cameron Crazies.

Duke (26-5, 13-3) shot nearly 46 percent - 51 percent in a dominant first half - and made eight 3-pointers in beating the Tar Heels at home for the first time since 2005 and wrapping up the No. 1 seed in next week's league tournament.

Freshman John Henson matched a season high with 14 points for the Tar Heels (16-15, 5-11), who had their lowest point total under coach Roy Williams and absorbed their worst loss in seven years.

``This is the first time that we've had to come in this locker room after a loss,' fifth-year senior Marcus Ginyard said. ``But the thing is, teams in the past found success here because we were tough enough and we came in and stuck it out through the times that weren't going our way and we made things go our way. And tonight we didn't do that. They were the aggressors on everything, and when it got tough, we allowed them to put it on us.'

Nolan Smith scored 20 points and Brian Zoubek continued his late-season surge with 13 rebounds for the Blue Devils, who took command with an early 31-8 run, led by 30 in the first half and showed no mercy in polishing off their first sweep of North Carolina since 2004.

``You never go into a game thinking you're going to blow somebody out by 30,' Scheyer said. ``But once we get a lead like that, we really want to have a killer instinct and put them away. I thought we never let off the gas.'

In some ways, this result was like so many others here this season. In setting a school record by finishing 17-0 at Cameron, Duke won all but one home game by double figures, and it entered with an average margin of victory here of 26 points. Just as they've done all year, the Blue Devils pounced early and never let up on their overmatched visitor, no matter who that opponent was.

But of course, for the Blue Devils, this one meant so much more - especially after the Tar Heels won their last four visits. North Carolina is the only visiting team in three full years to beat Mike Krzyzewski on the court that bears his nickname, and following last year's victory, some players flashed four fingers as they walked off the floor to mark their fourth win in a row at Cameron.

Already stewing from those defeats - and this week's loss at Maryland that kept them from clinching an outright ACC regular-season title - Duke's ``Big Three' made certain from the jump that there wouldn't be a fifth.

In the process, they made the opening half feel like a 20-minute-long burst by the Blue Devils.

Scheyer, Singler and Smith knocked down 3s on three straight trips downcourt to start the overwhelming run that put the Blue Devils in command. That spurt was so one-sided that by the time it ended, Duke had two players - Singler (12) and Smith (10) - who had outscored the Tar Heels (9).

``We told each other before the game (that) we need to have a game where the three of us start, every one of us start playing better,' Scheyer said. ``I thought that happened tonight, and it was a step in the right direction.'

The Blue Devils went up by double figures to stay 6 1/2 minutes into the game, stretched the margin to 20 on Smith's three-point play midway through the half and made it a 30-point game on Smith's free throw in the final minute of the half.

The only question in the second half was whether Duke would administer its most lopsided beating in the history of college basketball's fiercest rivalry: Ultimately, the Blue Devils fell shy of the 35-point drubbing they handed North Carolina in 1964.

``That was one of the best games we've played all year,' Krzyzewski said. ``The three veterans on the perimeter really set the stage in the first half with how they passed and moved with one another. ... I think we would have been tough to beat by anybody tonight.'

It was the Tar Heels' worst loss since a 96-56 loss at Maryland in 2003, and their fewest points since a 60-48 loss to Duke in the 2002 ACC tournament. Their No. 10 seed in the ACC tournament is their worst; the last time their record was this bad, the league had nine teams.

``There's not a lot you can say. We got our tails kicked,' Williams said. ``I told them if they take this and learn something from it and change, you can still get something. But if you just say, 'Oh, well,' you're not going to get anything from it.'

Deon Thompson had 11 points for the Tar Heels, who were serenaded by chants of ``NIT' throughout and played without freshman guard Leslie McDonald after team officials said he strained his right hamstring during Friday's practice.