Sanhedrin, Chapter Two, Mishnah One
Mishnah one contains with special rules regarding the High Priest.
1) The High Priest can judge and be judged; he can testify and others can testify against him.
2) He can perform halitzah for anothers wife and others can perform halitzah for his wife or contract levirate marriage with his widow, but he cannot contract levirate marriage since he is forbidden to marry a widow.
3) If any of his near kin die he may not follow after the bier, rather when the bearers are not visible, he is visible, when they are visible he is not visible, and he may go out with them as far as the city gate, according to Rabbi Meir.
i) Rabbi Judah says, He may not leave the Temple, as it says, Nor shall he go out of the Sanctuary.
b) And when he comforts other mourners the custom is for all of the people to pass by, the one after the other, while the appointed [priest] stands between him and the people.
i) And when he receives comfort from others, all the people say to him, Let us be your atonement, and he says to them, May you be blessed by Heaven.
c) When they feed him the funeral meal all the people sit around on the ground and he sits on a stool.
This mishnah can be divided into three basic sections: 1) the High Priests relationship to the court; 2) the High Priests ability to perform halitzah (the release of the widow from the obligation to marry the levir, her dead husbands brother) and levirate marriage; 3) the High Priests participation in the mourning ritual.
Section one: The High Priest is treated like a normal person with regards to the laws of the court. As we shall see in mishnah two, this is not true with regards to the king.
Section two: The High Priest is basically the same as any other person with regards to the laws of levirate marriage. If he should die without children, his wife must either marry his brother or his brother must perform halitzah for her. If his brother should die without children he must perform halitzah for his wife. He cannot, however, contract levirate marriage with her since he is in general prohibited from marrying a widow (Lev. 21:14).
Section three: The High Priest is severely restricted with regards to his participation in the rituals of burial. Since contact with the dead causes impurity the High Priest cannot even participate in the burying of his own immediate family (unlike a regular priest who may) (see Lev. 21:10-12). According to Rabbi Meir, the High Priest is allowed to semi-secretly participate in the burial procession, up until they leave the city gates of Jerusalem (people were not buried within the city confines). Rabbi Judah states that he may not even participate this much, since the Torah states that he may not leave the Sanctuary at all.
If the High Priest needs to participate in the comforting of mourners he may do so, but the appointed priest would come in between him and the other people. According to the Rambam this is to show the honor due to the High Priest, that he shouldnt be just a part of the crowd.
When others comfort him they say, Let us be your atonement. It seems to me that this is to assuage the sense of guilt that the High Priest must feel since he was not able to participate in the burying of his own dead. When he comforts others he should give them a blessing.
When he is fed the traditional funeral meal which would normally be eaten by the mourner while sitting close to the ground, the rest of the people must sit on the ground. This fulfills two functions: 1) he retains a higher status than them; 2) they are able to participate in his sorrow and grief.