Gemara

(Mishnah): Outside the Mikdash, Birkas Kohanim is said as three Berachos. In the Mikdash, it is said like one.

Sotah 39a (R. Zeira): The Korei may not call until the Tzibur finishes answering Amen (to Modim). The Kohanim may not bless until the Korei finishes. The Tzibur may not answer Amen until the Kohanim finish the Berachah. The Kohanim may not begin the next Berachah until the Tzibur finishes answering Amen to the previous Berachah.

Berachos 34a (Mishnah): The Shali'ach Tzibur does not answer "Amen" after Birkas Kohanim, lest he get confused.

If he is the only Kohen, he does not recite Birkas Kohanim.

If he is sure that he can recite Birkas Kohanim and resume the prayer, he may do so.

Rishonim

Rif, Rosh and Rambam (Megilah 15b and 3:21,23 and Hilchos Tefilah 14:5): The Korei may not recite until the Tzibur finishes answering Amen.

Rambam (3): The Kohanim ascend to the Duchan, turn around to face the people and begin Yevarechecha. Afterwards, the Shali'ach Tzibur is Makreh (says, for the Kohanim to repeat) word by word, and they answer, for it says "Emor Lahem" - they must wait for someone to say to them. When they finish the first verse, everyone answers Amen. The Shali'ach Tzibur returns and is Makreh the second verse word by word and they answer until they finish the verse, and everyone answers Amen, and similarly for the third verse.

Rambam (8): The Kohanim do not begin to bless until the Shali'ach Tzibur calls 'Kohanim'. They answer "Yevarechecha", and he says every word before them.

Rosh (21): R. Tam says that the Shali'ach Tzibur may not call to the Kohanim. He may not interrupt Shemoneh Esre even for Amen Yehei Shmei Raba! Rather, the Chazan (overseer of the Beis ha'Keneses) calls them. It says 'the Kohanim may not bless until the Korei finishes', and 'the Shali'ach Tzibur may not begin...' because the Korei is not the Shali'ach Tzibur. Also R. Chananel and Medrashim say so. However, the Shali'ach Tzibur may say the words for the Kohanim to repeat.

Tosfos (Berachos 34a DH Lo): The Mishnah says that the Shali'ach Tzibur does not answer "Amen" after Birkas Kohanim, lest he get confused. It should be forbidden due to a Hefsek (interruption) in his Tefilah! This implies that it is not a Hefsek, since it is a need of Tefilah. However, R. Tam says that to call the Kohanim to the Duchan is a Hefsek. Rather, someone else in the Tzibur calls them. In Sotah, we say that when there are two Kohanim, he calls them. It does not refer to the Shali'ach Tzibur, rather, to the Chazan, like it says in the Sifri. The Chazan is not the Shali'ach Tzibur. Rather, he deals with needs of the Tzibur. 'The Kohanim may not bless until the Korei finishes', i.e. the one who calls 'Kohanim.' Similarly, the Shali'ach Tzibur may not be Makreh. However, Rabbeinu Yehudah brings from a Medrash that the Shali'ach Tzibur says every word before the Kohanim. Some say that even R. Tam would permit. R. Tam said that it is a Hefsek only in their days, when immediately after Modim they did not say "Elokeinu... Borcheinu bi'Vrachah... (Kohanim).' Sotah 39b connotes like this. It forbids the Korei to be Makreh until the Tzibur finishes answering Amen, i.e. Amen to Modim. This shows that they said only 'Kohanim', immediately. Nowadays that we say Elokeinu..., this is like a Berachah or Tefilah. It is not a Hefsek. It is no worse than answering Amen, which is not a Hefsek.

Ran (Megilah 15b DH v'Ein): The Kohanim may not begin a Berachah until the Korei finishes the word. This refers to the word of calling the Kohanim. Others explain that they used to be Makreh to the Kohanim, lest they err. The Shali'ach Tzibur would say each word before they did.

Maharam Mintz (12): The Rambam says that if one Kohen blesses, he begins to bless by himself, and the Shali'ach Tzibur is Makreh word by word. 'He begins to bless' connotes Asher Kidshanu bi'Kedushaso Shel Aharon... It does not mean Birkas Kohanim, i.e. that he begins Yevarechecha by himself. He says afterwards that the Shali'ach Tzibur is Makreh. However, this is not an absolute proof. It could refer to Birkas Kohanim, and teach that he says the first word Yevarechecha by himself. After this, the Shali'ach Tzibur is Makreh word by word. Regarding two Kohanim, the Rambam connotes that he is Makreh only after the word Yevarechecha. He said that they say Yevarechecha, and the Shali'ach Tzibur is Makreh. He did not say in the reverse order, that the Shali'ach Tzibur is Makreh, and they say Yevarechecha. Even if the Rambam holds that we are not Makreh Yevarechecha to two Kohanim, it is unreasonable to say so about one. Since we call 'Kohanim' to two, it is as if we told them to say Yevarechecha. We do not call one Kohen Why should Yevarechecha be different than other words?

Poskim

Shulchan Aruch (OC 128:13): The Kohanim begin to say Yevarechecha...

Magen Avraham (20): When there is only one Kohen and they do not call 'Kohanim', all agree that the Shali'ach Tzibur is Makreh Yevarechecha. Maharam Mintz (12) says so.

Kaf ha'Chayim (83): Keneses ha'Gedolah did not understand the difference between one Kohen and two. Some places are not Makreh Yevarechecha in either case. The Acharonim say like Maharam Mintz.

Gra (DH Matchilin): We say that Kohanim may not begin until the Shali'ach Tzibur is Makreh. I.e. they may not begin Yevarechecha until the Korei finishes 'Kohanim'. (We do not refer to beginning the Berachah 'Asher Kideshanu...', for) this Berachah is not essential according to letter of the law. R. Elazar ben Shamu'ah said that one of his merits to live so long was that he never gave Birkas Kohanim without this Berachah. If letter of the law it were required, what is so special about this?!

Kaf ha'Chayim (82): The Mechaber is like the Rambam. The Beis Yosef and Rema bring the opinion of the Tur and Ran, that they must be Makreh also Yevarechecha. Tosfos agrees, for he brings the Medrash that learns from Emor Lahem. Also R. Bechaye (Bamidbar 6:23 DH v'Od Yesh) learns from Emor Lahem. The Ben Ish Chai says that it is proper to rule like this.

Rema: Some say that the Shali'ach Tzibur says also Yevarechecha before the Kohanim. (This is the custom in our lands.)

Beis Yosef (DH v'Shali'ach): The Tur holds that the Shali'ach Tzibur says even Yevarechecha before the Kohanim. It seems that the Ran agrees. Some say that they are Makreh to the Kohanim lest they err. The Kohanim may not begin even the first word by themselves, even though there is no concern for error, and all the more so the other words, until the Korei finishes the word. The Rambam connotes we are not Makreh the word Yevarechecha. One could explain that the Rambam to mean that they begin Yevarechecha after the Shali'ach Tzibur is Makreh, for he says that we are Makreh the first verse, and Yevarechecha is included. We could explain similarly in Halachah 8, that when there are at least two Kohanim, the Shali'ach Tzibur calls Kohanim, and they answer and say Yevarechecha. This would equate the Rambam to the Poskim, and to our text of Perush ha'Mishnayos. However, in Eretz Yisrael and Mitzrayim the custom is that Kohanim begin Yevarechecha by themselves. They are Makreh starting only from the second word. They say (in Eretz Yisrael and Mitzrayim) that they follow the Rambam. This is like the simple reading of the Rambam. They say that the original Perush ha'Mishnayos in Arabic is like this. Since there is no chance for error, there is no need to be Makreh the first word.

Gra (DH v'Yesh): This opinion holds that the Gemara means that they may not begin Asher Kideshanu... until the Korei finishes.

Shulchan Aruch (ibid.): Afterwards, the Shali'ach Tzibur is Makreh word by word, and they answer each word until they finish the first verse. Then the Tzibur answers Amen, and similarly after the second verse, and after the third verse.

Mishnah Berurah (49, citing the Pri Chodosh): This opinion expounds "Emor Lahem" to obligate being Makreh. In any case it is only l'Chatchilah. It is not Me'akev. A proof is Sa'if 25. In a Beis ha'Keneses of all Kohanim, (if there are only 10, all of them ascend to the Duchan and give Birkas Kohanim, even though there is no Makreh). Also, the Shali'ach Tzibur must be Makreh from a Sidur, and not by heart.

Bi'ur Halachah (DH v'Achar): Nehar Shalom rejected the Pri Chodosh's proof from Sa'if 25. There, the Shali'ach Tzibur is Makreh! It seems that all of them ascend to the Duchan, i.e. except for the Shali'ach Tzibur. The Pri Megadim explains like this. The Pri Chodosh held that it is a proof, for in Sa'if 20 he holds, unlike Hagahos Maimoniyos, that if a Shali'ach Tzibur Kohen is sure that he will be able to resume the Tefilah, he may Duchan even if there are other Kohanim. 'All' includes the Shali'ach Tzibur, i.e. in a case that he is sure. According to the Shulchan Aruch, 'all' does not include the Shali'ach Tzibur, so he has no proof. In any case, perhaps his law is true.

Kaf ha'Chayim (85): Many Poskim hold like the Pri Chodosh, including Teshuvos min ha'Shamayim.

Kaf ha'Chayim (87): Also, we answer Baruch Hu u'Varuch Shemo when the Kohanim say Hash-m's name.

Shulchan Aruch (OC 128:18): The Kohanim may not begin "Yevarechecha" until the entire Tzibur finishes answering Amen to Asher Kidshanu. They may not say a word before the one reciting it for them finishes. The Tzibur may not answer Amen until the Kohanim finish the Berachah.