Gemara

(Mishnah): One may not roast Pesach [on a metal spit or griddle].

74a: When part of a metal spit gets hot, all of it gets hot. [The inside of] the animal is roasted through the spit, and not through fire.

30b (Rav Ashi): [For Pesach,] I cover the [wooden] handles of my knives in mud and put the blade in fire. Then I do Hag'alah on the handles (Kasher them in boiling water).

The Halachah is, it suffices for the blade and handle to be in boiling water in a Kli Rishon.

(Rav Huna brei d'Rav Yehoshua): One may Kasher a wooden mixing spoon in boiling water in a Kli Rishon.

He holds that k'Bol'o Kach Polto. (The same way it absorbs, it emits.)

Zevachim 96b - Question (R. Yitzchak bar Yehudah): If Kodshim were cooked in part of a Kli, is Merikah u'Shtifah (scouring and rinsing) required for the part that was not over the fire?

Answer (R. Yitzchak): Yes. Cooking spreads absorptions through a Kli;

(Beraisa): If Kodshim were cooked in part of a Kli, the entire Kli requires Merikah u'Shtifah.

(Abaye): This is only for Kodshim. For Terumah, only that part requires Merikah u'Shtifah.

Rishonim

Rosh (Avodah Zarah 5:34): Rivam obligates Libun (heating until it glows) for old knives bought from Nochrim, for they use them to fix wicks in lamps of burning Chelev and turn over meat on coals. R. Tam says that since this is not its [normal] usage, we are not concerned lest it occurred. Even if it did, since the Yisrael does not use it with fire [without water], Hag'alah suffices. Whatever it will emit through Roschin (boiling water), it emits the first time. This is wrong. Since it is used through fire, Hag'alah without Libun does not purge the Isur. It emits [some] Isur in every Hag'alah, just like earthenware does not emit everything the first time. The Isur never leaves the walls. It emits a little each time. Do not distinguish, and say that what it absorbed through fire comes out only through fire. We do Hag'alah on a spit or grill of Kodshim! This shows that what it absorbed through fire comes out through Hag'alah. It seems that it suffices to do Libun on the blade of the Nochri's knife, for he uses the blade in the lamp. Even though if part is hot, all is hot, and the Isur spreads, the Yisrael does not use it with fire so this suffices.

Ran (8a DH v'Hani): Rav Ashi holds that knives are used with fire (without water), like a spit, and also with Roschin. The former usage does not reach the handle, but the latter use does. One puts the blade in fire due to the former, and the handles in boiling water due to the latter. We learn from here that if only part of a metal Kli is used, it suffices to Kasher that part, like we Kasher [only] the blade through fire. If Kodshim were cooked in part of a Kli, the entire Kli requires Merikah u'Shtifah. This does not apply to Terumah.

Note: One opinion says that Merikah u'Shtifah are in cold water, and one says that Merikah is in hot water (Zevachim 96b).

Ran (DH ud'Amrinan): If Pesachim, we say that if part gets hot, all gets hot. That refers to roasting Pesach, lest it be roasted through something (the spit) other than the fire. Here, it suffices to Kasher the part used. Some say that since the entire Kli becomes hot, one must Kasher all of it. Here, we rely on the Hag'alah he does at the end. Some texts say "he puts the Kli and the handles in boiling water." This is wrong. If so, putting the blade in fire did not help at all!

Poskim

Shulchan Aruch (YD 121:6): Some say that for a metal Kli, if part was used with Isur, the entire Kli is forbidden, because if part is hot, all of it is hot. Even so, one must be Machshir the entire Kli, whether through Hag'alah or Libun.

Beis Yosef (DH Kasav): The Rashba (in Toras ha'Bayis) says that for any metal Kli, if part is hot, all is hot. Therefore, even if only part was used with Isur, the entire Kli is forbidden. Even so, one must be Machshir the entire Kli, whether through Hag'alah or Libun. The Ran says that it suffices to be Machshir part of the Kli. The Rashba disagrees, for he obligates Hag'alah on knives and their handles. It seems that the Rosh holds like the Rashba. He says that it suffices to do Libun on the blade of the Nochri's knife, for Nochrim normally use [only] the blade with fire. Even though if part is hot, all is hot, and the Isur spreads, the Yisrael does not use it with fire, so this suffices. This connotes that one may not use it with fire, for we say "if part is hot, all is hot" only to forbid, but not to be Machshir. Since the Rosh and Rashba agree, we hold like them.

Shach (16): The Mechaber connotes like the Rashba, and he wrote like this in the Beis Yosef. The Rema should have said "some say...", to show that he argues. However, one could understand the Mechaber to discuss one who used the entire Kli. Therefore, the Rema wrote Stam. He does so in many places. The Rashba agrees regarding a Kli that absorbed Heter, e.g. milk.

Rema: This is only if he used the entire Kli.

Taz (7): This is from the Tur, who argues with the Rashba, who is like the Mechaber in this Sa'if. Why does the Rema connote that all agree to his words? Clearly, the Tur argues with the Rashba.

Suggestion: The Tur holds that the Rashba requires being Machshir all of it only if all of it was used, but if he used part, it suffices to be Machshir that part!

Rejection (Taz): The Rashba explicitly says unlike this in Toras ha'Bayis ha'Aruch and Mishmeres ha'Bayis. If Kodshim were cooked in part of a Kli, we require Merikah u'Shtifah for the entire Kli, but for Terumah, only for the part that was over the fire (Zevachim 96b). The Ro'oh (Bedek ha'Bayis) holds that Chulin Isurim are like Terumah. Hag'alah on the part that touched Isur suffices, because k'Bol'o Kach Polto. However, when we require Libun, one must do so to the entire Kli. Libun does not cause the Isur to leave. Rather, it eradicates (burns) the Isur. This is only on the part in which Libun is done. Hag'alah causes the Isur to leave. It leaves the entire Kli. The Rashba says that there is no proof from Zevachim to a Kli that absorbed real Isur such as Nevelah. He limits the leniency of Zevachim to absorptions of Heter, e.g. meat or milk. After Hag'alah, the taste of the meat is weakened, so the Isur of [meat and] milk does not take effect afterwards. If a Kli absorbed real Isur such as Nevelah, one must do Hag'alah on all of it. This is why one must do Hag'alah on knife handles for Pesach.

Shach (17): The Drishah and Bach explained the Rosh in a difficult way to resolve the Rosh with the Tur. I explain the Rosh simply. The Tur holds like the Ro'oh. Libun eradicates the Isur, but only on the part on which Libun is done. Hag'alah causes the Isur to leave the entire Kli. The Rosh discusses Libun. Even so, one may use the part not Kashered, just not with fire. The Ro'oh could agree. The Tur did not explicitly say so. He relied on what he wrote k'Bol'o Kach Polto, which applies only to Hag'alah. Perhaps the Rema agrees about Libun. This is unlike the Levush, who says that the Rema holds that Libun on part suffices.

R. Akiva Eiger (DH Aval): When one does Libun on part of the Kli, we do not say that the heat spreads the absorption. Heat of the Kli does not spread it without liquid.

R. Akiva Eiger (DH deha'Isur): If one end of a spit absorbed meat, and the other end was inserted into milk, even though the absorption spread, the absorption at the other side is Nosen Ta'am bar Nosen Ta'am (very weak) of Heter [so it does not forbid] - Mishbetzos Zahav (451:17). I say that this requires investigation.

Gra (17): Zevachim 96b connotes that they cooked only in part of the Kli. The Ran and Tur say so, unlike the Beis Yosef brings from the Rashba. One can read the Mechaber either way. See OC 451:12 (below). The Rema rules that we do not say if part is hot, all is hot. Here, he wrote k'Bol'o Kach Polto just to include the latter opinion. (Even that opinion admits that it suffices to Kasher part.)

Shach (17): Through the fire, the absorption spreads through the entire Kli.

R. Akiva Eiger (DH Molich): This is only if it (the roasted meat) was fatty. If it is lean, only Kedei Netilah (the thickness of a finger) of the Kli is forbidden. Perhaps we are not experts about this, like the Shach (105:23) says about absorptions from Kli to Kli.

Rema (ibid.): If he knows that he used only part, k'Bol'o Kach Polto.

Shach (18): L'Chatchilah one must be Machshir the entire Kli, like the Rema wrote in OC 451:10. Also Maharshal and Isur v'Heter say so.

Shulchan Aruch (OC 451:12): One must Kasher the handles of all Kelim like the Kelim.

Mishnah Berurah (68): 'If part gets hot, all gets hot' applies only to metal.

Rema: If one did not Kasher the handles, we do not forbid b'Di'eved.

Gra (DH Mihu): The Mechaber (121:6) rules like the Rashba. Even if one used only part, he must be Machshir all of it. The Rema explained like the Tur, who disagrees, because k'Bol'o Kach Polto. Why did the Rema need to say so? In YD (94:1, 98:4), he does not say "if part gets hot, all gets hot"! There, Hag'alah in one place will not purge absorptions elsewhere in the Kli. To absorb, he says "if part gets hot, all gets hot", like Tosfos. This is not only for metal Kelim. However, for a metal Kli if part gets hot, all gets hot even if only one part is near the fire, unlike the Shach (121:17), who said "we hold like this in YD 94." (He holds that only the part submerged in the pot absorbs.)

Gra (DH Ein): The Tur and Rema (YD 121:6) connote that this is even if he used the side on which Hag'alah was not done.