Section 502 - Trial by jury; waiver or withdrawal1. Right to jury trial. A party is entitled to trial by jury, if duly demanded, in any proceeding in which any controverted question of fact arises as to which any party has a constitutional right of trial by jury, in any proceeding for the probate of a will in which a controverted question of fact arises, and in any proceeding commenced after the death of the creator of a revocable lifetime trust to contest the validity of such trust in which a controverted question of fact arises.2. Demand for jury. (a) Cases initiated in the court. Each respondent demanding a jury trial must do so in his answer or objections. A petitioner who desires a jury trial must, without regard to whether or not an answering or objecting respondent has made such demand, serve and file in his own behalf a demand for jury trial within 6 days after the service upon him of an answer or objections.(b) Cases transferred to the court. In an action transferred to the court under 501, subdivision 1, a party who has duly demanded a trial by jury in the court from which the case is transferred shall be deemed to have duly demanded it in this court. If the party moving such transfer has not so demanded a trial by jury and shall not have waived such right or his time to make such demand has not expired he shall do so in his moving papers. Any other party to the transferred action who has not demanded a trial by jury in the court from which the case is transferred and shall not have waived such right or his time to make such demand has not expired must serve and file with this court a demand for a trial by jury within 10 days after the service upon him of a copy of the order of transfer with notice of entry thereof.3. Jury fee. The jury fee shall be paid by each party who demands a trial by jury.4. Order framing issues. After joinder of issue an order framing the issues to be tried shall be submitted on notice by any party. The court may direct any party to submit an order framing issues. The court shall make an appropriate order, a copy of which shall be served by the party submitting it on all parties who have appeared and pleaded.5. Waiver or withdrawal. (a) Waiver. A party waives the right to a trial by jury by:(i) failing to make a demand under subdivision 2;(ii) failing to appear at the trial;(iii) filing a waiver signed by him or his attorney with the clerk of the court; or(iv) orally waiving a trial by jury in open court or at any pre-trial conference, if entered in the minutes taken at the time.(b) Withdrawal. A party may withdraw a demand for a trial by jury without the consent of the other parties.6. Advisory jury. The court may submit any issue of fact to an advisory jury as provided in the CPLR. Upon the motion of any party or on its own initiative the court may confirm or reject in whole or in part the verdict of an advisory jury; may make new findings with or without taking additional testimony and may order a new trial. The motion shall be made within 15 days after the verdict. Where no issues remain to be tried the court shall file its decision in writing.7. The court may direct that any jury trial be had before it or at a trial term of the supreme court to be held within the county or if there be a county court in such county, in that court. The verdict if not set aside by the court before which the question is tried, shall be certified to the surrogate's court by the clerk of the court in which the trial took place and shall be conclusive except upon appeal.N.Y. Surr. Ct. Proc. Act Law § 502