What’s in a name? When the name is that of a famous artist, the answer can be millions of dollars. So it’s small wonder that disputes over the authenticity of artworks can be heated — and as prices have risen, particularly for 20th-century art, more of those disputes have ended up in court.

Currently, several lawsuits, brought by collectors or dealers against artists’ estates or so-called “authentication committees,” are pending in New York City courts.

The most recent suits, against the Jean-Michel Basquiat authentication committee and the Alighiero Boetti Archive — an organization run by relatives of the late Arte Povera artist — raise difficult questions about the powers and responsibilities of such committees, such as: What happens when a committee doesn’t render a decision about a work’s authenticity? And how often is it reasonable for a committee to change its mind?

The suit against the Basquiat committee involves a painting called “Fuego Flores,” which the plaintiff, a Swedish collector named Gerard de Geer, purchased in 1987. The dealer who sold it to him had bought the painting four years earlier from another dealer, who said he purchased “Fuego Flores” directly from the artist and who included it in a 1983 Basquiat exhibition at his gallery. (Basquiat died in 1988.)

In 2005, Mr. de Geer submitted an application to the Basquiat authentication committee, paying the $100 application fee. The committee responded a month later that it did not have enough information to make a decision and asked for an opportunity to see the work. Mr. de Geer provided such an opportunity, but to no avail: The committee still couldn’t make up its mind. Mr. de Geer submitted another application, with additional provenance information, but, again, no dice.

Mr. de Geer’s lawyer, Stephen Younger of Patterson Belknap Webb & Tyler, argues that, by accepting Mr. de Geer’s application fee, the committee entered into a binding contract, and that, by failing to reach a decision, it breached that contract.

The complaint demands that the committee either reach a decision or pay damages of up to $15 million. And in case the committee responds by declaring that the work is not authentic, the complaint also names as defendants both the dealer who sold Mr. de Geer the painting, Carl Flach, and the dealer who sold it to him, Stellan Holm. If the painting is fake, he argues, they are guilty of negligent misrepresentation and owe him $10 million.

The four members of the Basquiat committee — the artist’s father, Gerard Jean-Baptiste Basquiat, the dealers Jeffrey Deitch and John Cheim, and the collector Larry Warsh — either did not respond to calls or declined to comment. The lawyer for the committee, James Cinque, did not return several messages.

Meanwhile, a respected Manhattan gallery, Sperone Westwater, has sued the Boetti Archive in federal court in Manhattan for what it alleges is a broad scheme to discredit it by capriciously questioning the authenticity of works it has sold. Sperone Westwater’s suit follows a suit brought by the archive against the gallery in Milan, in which the archive seeks declaratory judgment that it is not liable to the gallery for not authenticating the works in dispute, and additionally claims that the gallery violated its “moral rights” by exhibiting, publishing, and selling works of art attributed to Boetti.

The story is tortuous, but the basic gist is this: In 2002, eight years after the artist’s death, Sperone Westwater presented an exhibition of 15 Boetti works. It sent the catalog of the show to the archive, which contacted the gallery to express concern about one of the pieces. After a representative of Sperone Westwater took the work to Italy so that the archive’s staff could examine it in person, the archive declared the piece to be not authentic, and the gallery removed it from the show.

The archive made no comment at the time about the other 14 works in the exhibition, of which Sperone Westwater sold nine. Beginning in 2004, however, the archive started questioning the authenticity of some of the other works the gallery had sold, including one that was purchased by the Art Institute of Chicago. It also effectively nullified a certificate of authenticity it had previously issued for a piece the gallery had sold, asking the gallery to send the work to Rome so that the archive could re-examine it, as the complaint says, “in light of alleged ‘episodes of counterfeited works.'”

There are more details, but, suffice it to say, these seeming vagaries made Sperone Westwater pretty mad. It threatened to sue, but the archive beat it to the punch by bringing the action in Milan. In the New York suit, Sperone Westwater asks the judge to make a declaratory judgment that the Archive has no moral rights claims and also seeks damages “for the Defendants’ injuries to the Gallery’s business and reputation,” on counts of breach of implied covenant of good faith and fair dealing, negligent misrepresentation, and interference with business relations.

The lawyer for the archive, Ronald Spencer of Carter Ledyard & Milburn, said that authentication committees must always reserve the right to change their opinions in response to new facts and new scholarship. Referring to another of his clients, the Andy Warhol Art Authentication Board, which is the target of another pending lawsuit, Mr. Spencer said: “The Warhol authentication board’s form expressly provides that the board may change its opinion when new facts and events come to light.”

Still, given the power that authentication boards hold over the market in an artist’s work, what responsibilities do they have to applicants and collectors? Several committees refuse to explain a decision that a work is inauthentic, on the grounds that doing so would provide useful information to forgers. But if a committee is divided on a work’s authenticity, would it not be reasonable to at least explain its split decision? A maybe-Basquiat would still be salable, if not for the millions that a real Basquiat would bring.

But it may be for players in the art world — rather than judges — to pressure authentication committees to be more transparent about their workings. A judgment came down yesterday in another case, brought by the owner of a stage set allegedly designed by Alexander Calder against the Calder Foundation, which after 10 years has not responded to his request to determine the work’s authenticity.

As in the Basquiat suit, the lawyer in this case, Richard A. Altman, alleged that the foundation had entered into a contract with the applicant, a musician and conductor named Joel Thome. But the judge didn’t buy it. He granted the defendants’ motion to dismiss, saying that accepting Mr. Thome’s application did not constitute a binding contract.