For those curious, the blog Notes on Arab Orthodoxy has translated the statutes dealing with the election of a new patriarch of Antioch.
Section Three of the Statute of the Greek Orthodox Church of Antioch
Paragraph 32: The candidate for the office of patriarch should be one of the members of the Holy Synod who has worked in it for a period of at least five years.
Paragraph 33: The office of patriarch shall be considered vacant in the event of the patriarch's death, resignation, dismissal, or permanent disability.
Paragraph 34: In the case of death, the patriarchal vicar seals the patriarch's quarters and letters with red wax in the presence of the head of the patriarchal office and members of the community for whom it is convenient to be present. He arranges a register signed by those present. He then announces the patriarch's death by telegram to the bishops and metropolitans of the See of Antioch.
Paragraph 35: Twenty-four hours after the announcement of his death and the attendance of the metropolitans, those of them who are present gather under the leadership of the senior in order of consecration to elect one of them as patriarchal locum tenens.
Paragraph 36: The patriarchal locum tenens immediately announces his position to Church and civil authorities and announces the date of the funeral, indicating his election as patriarchal locum tenens...
Complete post here.