At the first news conference, Mr. Stern arrived to find a sign that read: ''Owner: Trump Ice Inc.'' He ordered the sign replaced with one that stated the city still owns the park site.

Mr. Trump's public relations firm, Howard J. Rubenstein & Associates, called Mr. Stern to invite him to a news conference at the site and Mr. Stern replied: ''Thank you for inviting me to my park.'' A deputy commissioner of Parks and Recreation was thrown off the site by one of Mr. Trump's security guards.

''See this railing?'' Mr. Trump asked on an inspection of the rink yesterday. ''Same railing Onassis had on his boat.'' Finishing far under budget meant he had enough money left for burnished teak railings, lots of ornamental wrought iron, massive renovation of the skate house and landscaping.

A visitor yesterday commented: ''The place looks almost too nice, like it's in Minneapolis. It could use a good coat of New York grime.'' MR. STERN said he was most impressed with Mr. Trump's work and that is was just his words that sometimes bothered him. ''Reporters would just keep badgering him to say we were all a bunch of idiots until finally he would,'' Mr. Stern said.

''I guess it says a lot about the city,'' said Mr. Trump at Thursday's grand opening, ''but I don't have to say what it says.''

Mr. Trump said the same approach could be used to overhaul the subway system, for example. The rink project has spurred much discussion about why private developers can accomplish a job cheaper, faster and better than the public sector, and Mayor Koch has called for changing some laws. At the opening a few potential mayoral candidates showed up to wonder aloud why the city couldn't do the job. One of them, Comptroller Harrison J. Goldin, wore his ice skates.

Mr. Trump produced a three-foot pair of scissors, real ones weighing 40 pounds, to cut the ribbon.

Perhaps because Mr. Trump was bringing his, city officials brought some cheezy imitation three-foot scissors. They didn't work. Mr. Koch couldn't get Mr. Trump's scissors to work either, but a spokesman for Mr. Trump said the Mayor just didn't know how to use them.