Mullane appeared specially to object to the statutory provision for notice, claiming that it was inadequate to afford the due process required by the Fourteenth Amendment.

The Surrogate overruled Mullane's objections, and entered a decree accepting the accounting and terminating any rights the beneficiaries may have had against Central Hanover for mismanagement of the trust.

Justice Jackson began his examination of the issues of the case by discussing the nature of the jurisdiction which the Surrogate's Court was exercising.

Mullane had argued that this was essentially an in personam action, and that the Surrogate could not exercise jurisdiction on out-of-state residents upon whom personal service had not been made.

Jackson did not explicitly determine what type of jurisdiction was being exercised here, but held that the Fourteenth Amendment applied to all of them regardless of how the state classified the action.

He further held that notice by publication was acceptable for missing or unknown parties, for those whose whereabouts could not be ascertained by due diligence, and for those whose future interests were too conjectural to be known with any certainty.