"The case drew national attention when a surrogate from Alaska refused to have an abortion after the fetus she was carrying was diagnosed with a serious heart problem."

"She eventually traveled to Texas and gave birth to the child over the initial objections of the parents, a couple from California.... On Tuesday, Justice Kagan, who oversees emergency filings from California, denied the surrogate’s request to block the lower-court ruling in the couple’s favor. She acted on her own without referring the matter to her Supreme Court colleagues. The justice’s order did not include an explanation, as is often the case when the court responds to such filings...."

From "Supreme Court Order Gives Parents Custody of Baby in Surrogacy Fight/A surrogate refused to have an abortion after the fetus was diagnosed with a serious heart problem. She asked the justices to block a court order giving custody to the biological parents" (NYT gift link).

Here's the emergency filing. The proceedings below are all in state courts, and much of the argument is about jurisdiction, but that's interwoven with the merits of the case — who gets the baby:

M.W. “g[ave] birth” to Baby G. in Texas, and per the ordinary operation of Texas law, would thereby be “established” as his mother. Tex. Fam. Code Ann. § 160.201(a)(1). This Court has upheld the constitutionality of such statutes that confer parentage without regard to genetics—even in cases like this with facts that “are, we must hope, extraordinary.” Michael H. v. Gerald D., 491 U.S. 110, 113 (1989). Once those rights are conferred by state law, they cannot be stripped away lightly. Even “[w]hen the State moves to destroy weakened familial bonds, it must provide the parents with fundamentally fair procedures.” Santosky v. Kramer, 455 U.S. 745, 753–54 (1982). That didn’t happen here. The California courts stripped away M.W.’s rights to the child she carried for 37 weeks as she fought to save his life from those who sought him dead. They did so in overt breach of due process by construing M.W.’s challenge to jurisdiction and forum as consent....

In Michael H., the Court upheld a California statute that conclusively presumed the husband of the mother is the father and barred the biological father from any legal right to the child. Justice Scalia, writing for the majority, noted that you can't expand everyone's "liberty interest" here: "to provide protection to an adulterous natural father is to deny protection to a marital father, and vice versa." That left the state to do what it wanted with its statutory law: "Our disposition does not choose between these two 'freedoms,' but leaves that to the people of California."

Does that mean the people of Texas can write a statute that gives a baby to any surrogate who manages to get to Texas to give birth? The biological parents filed their case in California, before the baby was born and the California court never considered the Texas statute. A Texas court was involved after the baby was born, but it gave full faith and credit to the California court's judgment.