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Normally the court will set the hearing but as the statute states normally 30 days is sufficient and that is stated in the statute below. "The citation shall be submitted by the proponent to the court within thirty days after the filing of objections."
New York Surrogate's Court Procedure Act § 1411
1. Whenever objections are filed to the probate of a will, the proponent shall submit to the court for issuance a citation returnable at a motion term of the court (a) reciting that objections have been filed to the will offered for probate and that such objections may be determined at a trial or at a hearing or conference on the return date or on a date to be fixed by the court, and (b) reciting the consequences of failing to appear set forth in the provisions of subdivision six of this section.
2. The citation shall be submitted by the proponent to the court within thirty days after the filing of objections. If the proponent fails to submit the citation, the citation may be submitted by an objectant or any other interested person.
3. The citation shall be issued to (a) each person named or referred to in the propounded instrument who has not appeared in the proceeding and whose interests would be affected by the outcome of the proceeding, and (b) such other persons as directed by the court.
4. The citation shall be served in accordance with the requirements of sections 307 and 308, except that service may be made by mail as therein provided upon any person whether or not a resident of this state. Proof of the service of the citation shall be made and filed in the court at least two days before the return date of the citation.
5. Each person to whom the citation must be issued, as provided in subdivision three of this section, may waive service of the citation. Each person who has waived or has been served under this section may appear personally or by filing a notice of appearance.
6. Any person who has waived or has been served under this section and who does not appear will not be entitled to further notice, and each objection filed may be determined at a trial or at a hearing or conference on the return date or on a date to be fixed by the court. If a settlement is entered into and agreed to by all parties appearing at the trial, hearing or conference, such settlement and any final determination by the court will be binding on all persons who have waived or have been served with process and who have failed to appear. Any person so failing to appear may be required to contribute to such settlement an amount which bears the same proportion to the total amount of the settlement as his or her interest in the estate bears to the aggregate of the interests in the estate of all persons required to contribute to the settlement.
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