Gemara

The Halachah is, anything said within Toch Kedei Dibur is like part of the previous matter, except for (Rashbam - designation for; Tosfos - acceptance of) idolatry, (blasphemy, divorce) and Kidushin.

Shevuos 32a (Mishnah): If both witnesses simultaneously denied knowing, they are liable.

(R. Yochanan): We need not establish this like R. Yosi ha'Galili, who says that two events can occur simultaneously. Rather, the latter denied Toch Kedei Dibur of the first, so it is like is a continuation of what the first said.

Bava Kama 73b: There are two measures of Toch Kedei Dibur. A Rebbi greets his Talmid 'Shalom Alecha.' A Talmid greets his Rebbi 'Shalom Alecha Rebbi v'Mori'. R. Yosi holds that within the longer time (to say four words) is a continuation, but within the shorter time (to say two words) is not.

Berachos 39a (R. Chiya): One must finish blessing ha'Motzi at the same time he cuts from the loaf.

(Rava): One must finish ha'Motzi before slicing from the loaf.

The Halachah follows Rava.

Rishonim

Rif and Rosh (Berachos 27b and 6:20): The Halachah follows Rava.

Rambam (Hilchos Berachos 4:10): One may not bless on any food or drink until it is brought in front of him. If he blessed and afterwards they brought it in front of him, he must bless again. If one took a food to eat it and blessed on it and it fell from his hand and was burned or taken by a river, he takes another and blesses, even if it is the same species. One may bless on water in a stream, even though he will not drink what is in front of him when he blesses, for he intends for what will come later.

Rosh (Berachos 6:20): The Yerushalmi says that if one blessed on a radish (in the ground), and it did not come to his hand, he must bless again.

Rosh (9:13): The Yerushalmi says that if one was in a privy and saw lightning, he leaves and blesses only if he can do so Toch Kedei Dibur.

Poskim

Shulchan Aruch (OC 206:3): Regarding all these Berachos, one may not interrupt between the Berachah and eating (Rema - more than Kedei Dibur).

Taz (3): This is the time for a Talmid to greet his Rebbi, 'Shalom Alecha Rebbi v'Mori.'

Kaf ha'Chayim (15): The Beis Yosef said so in the name of Shibolei ha'Leket, and also the Levush says so. Shirei Keneses ha'Gedolah says that this is a printing mistake. Really, it is the time to say three words, 'Shalom Alecha Rebbi.'

Note: Shinuy Nusch'aos in the Frankel Bava Kama/Sefer ha'Mafte'ach brings many opinions that the text on 73b includes the word 'v'Mori', and many opinions that it does not.

Beis Yosef (p. 320 DH V'Zeh, citing Shibolei ha'Leket 166): Rav Nisim Gaon says that if one blessed before doing a Mitzvah or before eating a food, and he was unable to do or eat it right away, and delayed a bit and did it later, he must bless again. Presumably, this refers to a delay Kedei She'alas Talmid l'Rav, which is the time to say 'Shalom Alecha Rebbi v'Mori.' The Yerushalmi says that if one was in a privy and saw lightning, he leaves and blesses only if he can do so Toch Kedei Dibur. This shows that Toch Kedei Dibur is not a Hefsek, but more than this is a Hefsek. This applies to one who blessed on a matter and could not do it immediately, or a Berachah that he was obligated to say but could not say immediately.

Beis Yosef (OC 140 DH Kosav): A case occurred in which the Ba'al Korei erred about which Parshah to read first. After the Kohen blessed, they told him of his mistake, and he rolled the Torah to the correct place. Some say that he needed to bless again. The Avudraham says that they learn from the Yerushalmi. If one blessed on a radish and it did not come to his hand (he could not pull it out by the leaves), and needed to (dig and) take it from the ground, he must bless again, for a long delay in silence is like a Hefsek of speech. The Avudraham disagreed. The Halachah follows Rabah (39b), that one blesses before cutting the bread. A delay in silence (while cutting), be it big or small, is not a Hefsek. However, the Poskim ruled that he must bless again, for this is like one who blessed on a food, and it fell, and he took another to eat.

Magen Avraham (4): Surely, l'Chatchilah one may not delay in silence. B'Di'eved, he need not bless again unless he spoke in between.

Mishnah Berurah (12): If he spoke one word in between not necessary for the Berachah, this is a Hefsek.

Mishnah Berurah (13): B'Di'eved, one need not bless again even if he delayed in silence for much longer than Kedei Dibur, as long as he did not divert his mind from the Berachah. One may not bless on a food or drink that is too hot to cold, due to concern for a Hefsek. If one wants to spill off a little water before drinking, he should do so before the Berachah, due to concern for a Hefsek and disgrace to the Berachah. One should break a nut before blessing on it, due to concern for a Hefsek. Also, perhaps he will find that it is not good.

Kaf ha'Chayim (22): Likewise, if one must remove something from a food before eating it, he must do so before the Berachah to avoid a Hefsek. Also, one should bless on something clean.

Kaf ha'Chayim (21): L'Chatchilah one may delay in silence if needed to eat the food. Therefore, one blesses on a whole fruit, and afterwards he cuts it.

Shulchan Aruch (5): One may not bless on a food or drink until it is brought in front of him.

Beis Yosef (DH Ein): This is unlike one who blesses on water in a stream (what he will drink is not in front of him, rather, upstream, when he blesses). Here, perhaps they will not bring to him.

Taz (6): The Kesef Mishneh says that this is due to the Yerushalmi brought in the following Halachah (if one blessed on a food and it fell and was lost, he must bless again).

Mishbetzos Zahav (6): The Yerushalmi asked, if one blessed on a food and it fell and was lost, must he bless again? This is unlike blessing on water in a stream, for there he intends for what will come later. R. Chiya taught that one blesses on bread only when he slices it. R. Chiya bar Vah learns from this that if one blessed on a radish, and was unable to pull it out, he must bless again. There are three explanations of this. The Rosh says that the question was settled. R. Chiya taught that one blesses on bread only when he slices it, lest it fall, for then he would need to bless again. R. Chiya bar Vah's law follows directly. Shibolei ha'Leket holds that the question was not settled. It is a Safek, and we are stringent. (This is not clear, for Berachos are mid'Rabanan, and saying Hash-m's name in vain is a severe Isur!) R. Chiya's law is a separate matter, due to a Hefsek, and R. Chiya bar Vah learns from it. The Beis Yosef explains that the question was settled from R. Chiya, who taught that one blesses on bread only when he slices it, lest it fall, for then he would need to bless again. R. Chiya bar Vah teaches a new matter, that if one blessed on something and afterwards they brought it to him, he must bless again. Since the Shulchan Aruch (Sa'if 3) brings the law that follows from Shibolei ha'Leket's explanation, what is the source for our Halachah? In Sa'if 3, the Shulchan Aruch only means that l'Chatchilah one should not delay, but b'Di'eved one does not bless again, like the Magen Avraham (4) says. The source is from reasoning, and not from the Yerushalmi.

Rema (296:1): We spill from the cup of Havdalah after Havdalah.

Magen Avraham (4): We spill after drinking from it, like I explained (it disgraces the cup to spill before drinking), and also to avoid a Hefsek.