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Chief Justice John G. Roberts Jr., the father of two adopted children, seemed sympathetic to Ms. Blatt’s clients and pressed Mr. Brown’s lawyer, Charles Rothfeld, about why he should win custody of Veronica in spite of his early renunciation of his duties as the father.

When Mr.  Rothfeld said Mr. Brown was excited to learn his girlfriend was pregnant, Chief Justice Roberts said, “He was excited, but there is no doubt he paid nothing during the pregnancy and nothing at the time of the birth, right, to support the child or the mother?”

Mr. Rothfeld began to answer: “That is true. But I, I am …” he said before Chief Justice Roberts cut him off.

The chief justice said: “So he was excited by it. He just didn’t want to take any responsibility.”

One outcome that seemed to have some appeal would be for the justices to order South Carolina courts to consider the case anew, with more of an emphasis on the best interests of the child. Paul Clement, representing a guardian appointed by the state to look out for Veronica, suggested such an approach.

“From the child’s perspective, the child really doesn’t care whose fault it was when they were brought in one custodial situation or another. They just want a determination that focuses on at the relevant time, that time, what’s in their best interest,” Mr. Clement said.

An evaluation of the child’s interest could well leave Veronica with her father, said Justice Ruth Bader Ginsburg. “Now the child has been some 15 months with the father. So if a best-interest calculus is made now, you would have to take into account uprooting that relationship, would you not?” she asked.

Mr. Clement agreed. “We’re not here to try to say that anybody is entitled to automatic custody of this child based on some legal rule,” he said.

A decision is expected by late June.

The case is Adoptive Couple v. Baby Girl, 12-399.