The case is Goldstein v. Pataki. Here's how the Court of Appeals summarizes the plaintiffs' claims:
The heart of the complaint . . . and the centerpiece of the instant appeal, is its far-reaching allegation that the Project, from its very inception, has not been driven by legitimate concern for the public benefit on the part of the relevant government officials. Appellants contend that a “substantial” motivation of the various state and local government officials who approved or acquiesced in the approval of the Project has been to benefit Bruce Ratner, the man whose company first proposed it and who serves as the Project’s primary developer. Ratner is also the principal owner of the New Jersey Nets. In short, the plaintiffs argue that all of the “public uses” the defendants have advanced for the Project are pretexts for a private taking that violates the Fifth Amendment.
The Supreme Court has interpreted the eminent domain provision of the Fifth Amendment to mean that "one person’s property may not be taken for the benefit of another private person without a justifying public purpose, even though compensation be paid.” The issue here is whether the Atlantic Yards Project is for a public or private purpose. After noting that the Federal courts have a limited role in second guessing the Legislature's determination that a taking is for a "public use," the Second Circuit rejects this eminent domain challenge because "viewed objectively, the Project bears at least a rational relationship to several well-established categories of public uses, among them the redress of blight, the creation of affordable housing, the creation of a public open space, and various mass-transit improvements."
In other words, the Circuit tells us, "the redevelopment of a blighted area, even standing alone, represents a classic example of a taking for a public use. Nor does it matter that New York has enlisted the services of a private developer to execute such improvements and implement its development plan. Once we discern a valid public use to which the project is rationally related, it 'makes no difference that the property will be transferred to private developers, for the power of eminent domain is merely the means to the end.'”
As for the plaintiffs' claim that the government's justification for eminent domain is pretextual, or mendacious, the Second Circuit reads Kelo to reject any pretextual challenge to a public taking. Of course, the court never says never: "a fact pattern may one day arise in which the circumstances of the approval process so greatly undermine the basic legitimacy of the outcome reached that a closer objective scrutiny of the justification being offered is required. In this area, 'hypothetical cases . . . can be confronted if and when they arise.'"