Gemara

Rav Ashi: I make my knives like new [for Pesach]. I cover the [wooden] handles in mud [lest they burn during Kashering] and put the blade in fire, then I put the handles [without the mud] 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): A wooden mixing spoon may be Kashered in boiling water in a Kli Rishon.

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

74a: When part of a metal spit gets hot, all of it gets hot.

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

Rif and Rosh (8b and 2:7): For Pesach, one puts knives with their handles in boiling water in a Keli Rishon.

Mordechai (577, 578): A wooden mixing spoon may be Kashered in boiling water, even the handle. If a Kli with a patch absorbed Isur, one need not remove the patch when Kashering it. Every pot and frying pan has nails or a brim. [One need not remove it before Kashering, for] we say k'Bol'o Kach Polto. A proof is from knives. We Kasher them in boiling water. One need not remove the blade from the handle.

Ran (8a DH v'Hani): Rav Ashi holds that knives are used in two ways. They are used with fire (without water), like a spit, and also with Roschin (hot food cooked through water). 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. In Zevachim, we say that 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): In Pesachim 74a, 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!

Tosfos (96b DH Bishel): What was Rav Yitzchak's question? If part of the Kli is on the fire, and the rest is cold, he could not answer that cooking spreads absorptions. It does not spread through the entire Kli [where it is cold]! If the entire Kli is hot, surely absorptions spread through the entire Kli, and Merikah u'Shtifah is needed for the entire Kli! If he is unsure whether or not absorptions spread through the entire Kli, he should ask also about other Isurim (especially since in his day, there were no Kodshim - PF)!

Rashba (1:371): If Kelim have cracks or additional pieces, Kashering in boiling water purges the absorptions. Hag'alah purges absorptions from both [the Kli and the cracks] equally. However, we are concerned lest some of the Isur itself entered. Hag'alah does not Machshir Isur itself. In such a case, our custom is to put coals on the crack in order to burn any Isur that might be there before Hag'alah. The only solution for a wooden handle is to widen the crack and remove whatever is there.

Poskim

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

Bach (9 DH Kasav): The Tur brings that one cannot Kasher horn (ivory) spoons. If so, one cannot Kasher knives with an ivory handle through Hag'alah (Maharil). Some say that one cannot Kasher bone Kelim, for he is concerned [lest they get ruined], and he will not Kasher them properly (Mahariyo). I apply this to knives with bone handles, or even of wood. Since the handle is glued on, he is concerned.

Taz (17): The need to Kasher the handles is not because when part [of the Kli] gets hot, all gets hot. The Tur (YD 121) obligates Kashering the entire Kli only if he used the entire Kli! Rather, perhaps the handle [contacted and] received Chametz at some time, and now it will touch hot Matzah. (The Matzah absorbs a taste of Chametz. This is Min b'Mino, which is not Batel - PF.) Therefore, there is no difference between wood and metal Kelim. L'Chatchilah, one is Mag'il (does Hag'alah on) the handle. However, one should be stringent about a knife even b'Di'eved, since the Gemara explicitly requires Hag'alah for it, like I wrote above (5). Both [the knife and handle] require Hag'alah. If one did not do Hag'alah on the handle and he cut a hot food during Pesach, there is no source to permit b'Di'eved, for surely [food] touched the handle while using the knife. This does not apply to [handles of] other Kelim, such as a pan.

Gra (DH Kol): We say (30b) that one must be Mag'il the handles. On 74a, we say that when part gets hot, all gets hot (Rashba).

Mishnah Berurah (68): The Mechaber says so for all Kelim, even Cheres (earthenware) and wood. 'If part gets hot, all gets hot' applies only to metal. For a stirring spoon, we are concerned lest the handle received Chametz through a Kli Rishon when washing it. For a pan, perhaps drops splashed onto the handle from the Kli.

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

Magen Avraham (24): Isur v'Heter (58) says 'one must be Mag'il a pan handle. However, b'Di'eved one need not be so concerned. All the more so, one must be Mag'il a stirring spoon, for normally it is totally entered. Even if he did not [totally] enter it, if part gets hot, all gets hot. If part touched Isur, and he was Mag'il part, and it touched food, it is permitted.' I forbid if the part not Kashered touched food, like a drop of milk that fell on a pot (YD 92:5). L'Chatchilah one may not use it before totally Kashering it, even during Pesach when one cannot Kasher it.

Gra (DH Mihu): The Ran rejected [the first opinion, of the Mordechai]. If the entire Kli must be Kashered, Rav Ashi should have put also the handle in fire! Only for Kodshim one must Kasher the entire Kli. Also the Tur (YD 193:2) and Rema (YD 121:6) say so. However, Tosfos (96b) connotes that the entire Kli must be Kashered regarding all Isurim. The Rashba's text says "he is Mag'il the Kli and the handle." We rely on Hag'alah at the end. It is a mere stringency to put the blade in fire, like the Poskim say. See the Magen Avraham. The Mechaber and Rema rule like they wrote in YD 121. The Mechaber rules like the Rashba. Even if one used only part, he must be Machshir all of it (Mechaber 121:6). 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 does say "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.)

Mishnah Berurah (69): This is even for metal. Just like the handle absorbed through Guf ha'Kli, it was purged now through it. B'Di'eved, we are not stringent for the other concerns. If one was not Mag'il, inserting the handle forbids the food. This is Stam. If one know that he used the handle for hot Chametz, even b'Di'eved if he Kashered part, it is not enough. The Taz and others are stringent about knives, for Chametz usually touches them, e.g. hot bread.

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.

Kaf ha'Chayim (149): Eliyahu Rabah says that if the handle was inserted in hot food, b'Di'eved we rely on Hag'alah of Guf ha'Kli. R. Zalman permits b'Di'eved to avoid a big loss, or if needed for Simchas Yom Tov.

Kaf ha'Chayim (150): If it is a Safek whether or not the handle touched, since it is a stringency of Pesach to forbid Nosen Ta'am li'Fgam, this is a Safek mid'Rabanan, so we are lenient.

Rema: Even l'Chatchilah one may Kasher through Iruy (pouring boiling water on them).

Magen Avraham (25): Also the absorption was like Iruy, i.e. it went from one side to the other.

Gra (DH v'Afilu): It (the other part) does not become hotter than Iruy. Darchei Moshe brings from Isur v'Heter that l'Chatchilah it is good to do Hag'alah, for the entire year one touches it with dirty hands. However, through Iruy, l'Chatchilah [one may use it]. Many are lenient. L'Chatchilah, Hag'alah is better, like Isur v'Heter. This is unlike Magen Avraham [who says that Iruy is due to absorptions from the other side. Really, it is because hands touched it - Damesek Eliezer.] If one used all of it, all agree that he must Kasher all of it.

Kaf ha'Chayim (152): The Levush says that Iruy suffices because the absorptions are not so strong.

Mishnah Berurah (71): If one knows that he used the handle for hot Chametz in a Kli Rishon, Hag'alah is needed. Iruy does not help, even b'Di'eved.