A publication divorce in New York is a type of divorce where one spouse cannot be located or served with divorce papers. This occurs when a spouse is unable to be located, avoiding service, or living out of state or country. The process involves filing a divorce petition, attempting to serve the spouse, filing an affidavit of service, publishing a notice of divorce, filing proof of publication, waiting for the statutory period, and applying for a default judgment. The consequences of a publication divorce include loss of rights, default judgment, and limited appeal rights.