Yoma, Chapter 1, Mishnah 2. Continuing the discussion of the Kohen Gadol's preparations for Yom Kippur, the Mishnah goes on to detail the services he would perform during the seven days of separation, and afterward the rights of precedence he enjoys throughout the rest of the year.
The Kohen Gadol's service during the seven days of separation:
"Kol shivas hayamim hu zorek es hadam u'maktir es haketores u'meitiv es haneiros u'makriv es harosh v'es haregel" - throughout those seven days, during which he was separated and residing in the Beis HaMikdash, the Kohen Gadol himself would perform the services:
"Zorek es hadam" - he would sprinkle and dash the blood of the daily tamid offerings, the sacrifices brought in the morning and in the afternoon.
"Maktir es haketores" - the burning of the incense.
"Meitiv es haneiros" - the preparation of the lamps of the Menorah.
"Makriv es harosh v'es haregel" - placing the head and the leg of the animal upon the altar. These are the first two limbs of the offering, and the same applies to all the remaining limbs as well.
His rights during the rest of the year:
"U'she'ar kol hayamim im ratzah l'hakriv - makriv" - during the rest of the year, when there are no preparations for Yom Kippur underway, if the Kohen Gadol wished to be the one who offers the communal sacrifices, the offerings of the public, he is permitted to do so.
And the reason for this: "She'kohen gadol makriv chelek b'rosh" - the Kohen Gadol has the right of first choice in offering. He may offer the portion that he brings, and his precedence stands even over the watch whose turn it ordinarily is to offer.
"V'notel chelek b'rosh" - and likewise regarding eating: from all the sacred offerings that are eaten, he may choose first and take the portion he desires, ahead of any other kohen.
It is worth noting that this right was stated only with regard to offerings of the altar - items brought into the Beis HaMikdash as sacrifices. But with regard to things such as Terumah, challah and the other agricultural gifts given to the kohanim, he has no precedence over any other kohen.
In summary: in this Mishnah we learned that during the seven days of separation the Kohen Gadol would personally perform the daily tamid services - dashing the blood, burning the incense, preparing the lamps, and offering the head and the leg; and during the rest of the year he holds a twofold right of precedence: to offer a portion first, and to take a portion first from the sacred offerings that are eaten - and this applies to offerings of the altar alone.