In the case of Richardson v. Ainsa, Administrator of Ely in 1910, the Supreme Court was tasked with determining whether a will that had been probated in Arizona could be contested by an heir who lived outside of the state and did not participate in the original proceedings. The court ruled that due process rights were not violated when a state court adjudicated on matters concerning property within its jurisdiction, even if all interested parties were not present or represented during proceedings. This ruling was based on Pennoyer v. Neff (1877), which established personal jurisdiction principles under U.S law - specifically stating that courts have power over individuals and property within their territory but lack authority beyond it unless specific conditions are met.

In the dissenting opinion for the case of Richardson v. Ainsa, Justice Holmes disagreed with the majority's interpretation of a Spanish law that was in effect when Arizona and New Mexico were acquired by the United States. He argued that under this law, an illegitimate child could not inherit from their father unless they had been formally recognized by him. In this particular case, he believed there was no evidence to suggest such recognition had occurred before death. Therefore, according to Justice Holmes' interpretation of applicable Spanish law at that time period, it would be incorrect to allow inheritance rights for an unrecognized illegitimate child from his deceased father’s estate.