The New York Supreme Court handles divorce cases in all 62 counties of New York State, including uncontested and contested divorces, matrimonial actions, and family law matters. The process involves filing a divorce petition, serving divorce papers, discovery, mediation, negotiation, and trial. Grounds for divorce include irreconcilable differences, cruel and inhuman treatment, abandonment, imprisonment, and adultery. The average divorce timeline is 6-12 months, depending on the complexity of the case and conflict levels.