Will New Yorkers prefer Timbits over Munchkins? That taste test will begin this weekend when about a dozen Dunkin' Donuts stores in the city will be transformed into the first local outlets of Tim Hortons, the king of doughnut sellers in Canada.The Riese Organization, the company that first visited the urban food court upon Manhattan, is ending its affiliation with Dunkin’ Donuts and hoping it can make more money with a chain named after a dead hockey player. Mr. Horton, a six-time all-star in the National Hockey League, opened a doughnut-and-coffee shop in Ontario 45 years ago. He died in a car crash 10 years later, but the chain grew on.It now has more than 3,400 locations, including more than 500 in the United States, and its signature bite-size treats — Timbits — come in 35 varieties, including lemon-filled and sour cream glazed.Of course, the competition will be fierce. Dunkin’ Donuts, home of the Munchkin, has at least 500 locations in the New York City area alone, said Dennis Riese, chief executive of the Riese Organization. There are 427 within 10 miles of Times Square, according to the Dunkin' Donuts Web site. The nearest Tim Hortons is in Meriden, Conn., according to a spokesman for Riese.That will change at 6 a.m. Monday, when commuters will be surprised to find that their usual stop for coffee and breakfast has a new name, look and menu, Mr. Riese said. He said he decided to convert 13 stores in the city, including one in Pennsylvania Station, because he hopes the broader menu of Tim Hortons will attract more customers for lunch and dinner.Each of the restaurants has a kitchen, even though the doughnuts were made at a central commissary in Long Island City, Queens, Mr. Riese said. All of the food at the Tim Hortons, including the doughnuts, will be made on the premises, he said.The conversion comes after a decade of contention between Riese and Dunkin’ Donuts that peaked after the New York Post published a photo of a mouse munching on a doughnut in a shop operated by Riese on 46th Street at Fifth Avenue. The chain sued Riese and the sides eventually agreed that the relationship would end this week in what Dunkin’ Donuts called a “disenfranchisement.”The high cost of rent in Manhattan made it impossible to earn an acceptable profit from Dunkin’ Donuts, Mr. Riese said. “Dunkin’ is a great concept for a customer and a consumer,” he said, but added that “I can’t make money with them.”Mr. Riese admitted that it will be a challenge to sell an unfamiliar chain to New Yorkers, though he said he had already done it with Godfather’s Pizza shops. He said he was betting that Tim Hortons would have more staying power than Godfather’s or Krispy Kreme, the southern doughnut chain that stormed into New York at the start of this decade but has retreated, leaving just two locations near Penn Station.