Gemara

13a (Mishnah): If a man puts his hand to his Ever (to check himself), his hand is worthy to be cut off!

(Beraisa #1 - R. Eliezer): One who holds his Ever while urinating causes a Mabul.

Chachamim: If he does not hold it, drops will fall on his feet, and people will think he is a Seris (who is impotent), and they will say that "his" children are really Mamzerim!

R. Eliezer: It is better that people say that his children are Mamzerim than for him to sin, even for a moment.

(Beraisa #2 - R. Eliezer, to Chachamim): He can stand in a high place, or in a place of loose earth, so drops will not fall on his feet, and he will not sin, even for a moment.

He gave the latter answer first. Chachamim asked what to do if he does not find a high place or loose earth. R. Eliezer said "it is better that people say..."

Rav Yehudah and Shmuel were on the roof of a Beis ha'Keneses. Rav Yehudah needed to urinate. Shmuel told him to hold his Ever and urinate over the side.

Question (Beraisa - R. Eliezer): One who holds his Ever while urinating causes a Mabul.

Answer #1 (Abaye): Rav Yehudah's case was considered like a troop;

(Mishnah): If an army entered a city in wartime, even open barrels of wine are permitted, because the soldiers do not have time to pour to idolatry.

This is because they are afraid. Also here, Rav Yehudah was afraid, so he would not have Hirhurim (thoughts that could lead to an emission).

Question: Why was he afraid?

Answer #1: It was night. Perhaps he would fall off the roof.

Answer #2: His Rebbi (Shmuel) was there.

Answer #3: He feared the Shechinah (because he was over a Beis ha'Keneses).

Answer #4: Shmuel said that Rav Yehudah's fear of Hash-m (everywhere) was superhuman.

Answer #2: Rav Yehudah was married;

(Rav Nachman): A married man may hold his Ever (when urinating).

Answer #3: Shmuel permitted him to hold only the Beitzim from below, but not the Ever;

Aba, the son of R. Binyamin, taught a Beraisa that says so.

Answer #4: Shmuel permitted him to hold the Ever only from the crown and below, like R. Avahu taught.

40a (Mishnah): If a man was eating Terumah and felt his semen moving (it is about to come out), he should hold his Ever tightly (to delay the emission) until he swallows the Terumah.

Contradiction (Beraisa - R. Eliezer): One who holds his Ever while urinating causes a Mabul!

Answer #1 (Abaye): The Mishnah permits holding the Ever only through a thick cloth.

Answer #2 (Rava): He may use even a thin cloth. Once the semen starts moving, it will come out in any case.

Shabbos 118b: Rebbi (Yehudah ha'Nasi) was called Rabbeinu ha'Kadosh because he never put his hands below his belt.

Rishonim

Rambam (Hilchos Isurei Bi'ah 21:23): When a bachelor urinates, he may not hold the Ever. A married man is permitted. In every case he should never put his hand to his Ever, except when he needs to eliminate.

Rosh (2:1): Rav Nachman permits a married man to hold his Ever (when urinating). A Beraisa permits holding the Beitzim from below. R. Avahu permits holding the Ever only from the crown and below.

Tosfos (13a DH Ochez): What was the question from R. Eliezer? Chachamim argue with him! Perhaps they permit only due to concern for accusations of Mamzerus. Rav Yehudah was in a high place. He held the Ever just for honor of the Beis ha'Keneses, lest the urine fall on the wall. Alternatively, Chachamim retracted and agreed with R. Eliezer. In Berachos (40a) we say that the last drops come out only if one sits or in loose dirt or on a high place. We did not say 'or if he holds the Ever'! Below (16b), we say that Hash-m hates one who holds the Ever. R. Eliezer's name was not mentioned.

Tosfos (DH Im): Rebbi was called Rabbeinu ha'Kadosh because he never put his hand below his belt. The Chidush is that even though he was married, he was stringent.

Poskim

Shulchan Aruch (OC 3:14): One may not hold the Ever while urinating, only from the crown and below, for this (holding it above the crown) causes Zera l'Vatalah.

Beis Yosef (DH v'Yizaher): This is like R. Eliezer. Chachamim retracted and agreed with him (Tosfos).

Beis Yosef (DH u'Mah she'Chasav): Rashi explains that 'above' means towards the body.

Question: We find the opposite, that holding it warms it only if one holds the crown (from the Milah towards the ground)! Indeed, the Aruch explains that 'below' means towards the body.

Answer (Pe'ulas Tzadik 2:91): Each Mefaresh explained based on what he himself felt.

Note: Even though it is Midas Chasidus not to hold it even below the crown even for a married man, it is reasonable that in order to explain the Gemara correctly, the Meforshim experimented, e.g. just before relations with their wives.

Kaf ha'Chayim (39): The Magen Avraham and others permit holding it through a thick cloth. Bechor Shor and the Birkei Yosef permit a thick cloth only for a short time, e.g. while swallowing or checking, but not for the time to urinate.

Beis Yosef (DH v'Al): One may hold it below the crown even during an erection.

Kaf ha'Chayim (40): Kisei Eliyahu forbids during an erection.

Shulchan Aruch (ibid.): It is permitted only if he is married.

Beis Yosef (DH u'Mah she'Chasav Rabeinu): It seems that Rav Nachman and R. Avahu do not argue. Each agrees with the other. If so, Rav Nachman permits a married man even above the crown. If he permits only below, why did he mention a married man? Even a bachelor is permitted below! It seems that the Rambam holds like this. He permits a married man Stam. It seems that Semak agrees. I thought to correct the Tur to say like this, but in Even ha'Ezer he said 'I wrote in Orach Chayim that even a married man is permitted only below the crown.' He must hold that Rav Nachman argues with R. Avahu. Rav Nachman distinguishes only between a married man and a bachelor. R. Avahu permits both only below the crown. The Tur rules like R. Yochanan. This is astounding. The Rosh brought both Rav Nachman and R. Avahu, and also the Rif (Shabbos 39b brought the entire Sugya). This implies that they hold that Rav Nachman and R. Avahu do not argue! What forced the Tur to say that they argue? The Rambam did not mention holding it below the crown. Perhaps also he holds that they argue, and he rules like Rav Nachman, for he is Basra.

Kaf ha'Chayim (41): The Shulchan Aruch permits even a bachelor below the crown (Nevei Shalom, Shev Yakov). Olas Tamid was unsure about this.

Shulchan Aruch (ibid.): It is Midas Chasidus not to do so even if he is married.

Beis Yosef (DH v'Achar): R. Yonah (Sefer ha'Yir'ah) permits even a married man only below the crown; since the punishment is so great, one should sanctify himself and refrain even from what is permitted. Rabbeinu ha'Kadosh never put his hand below his belt. It seems that the Tur holds like R. Yonah, just he was concise and did not say that this is only Midas Chasidus.

Rebuttal (Taz 13): In Even ha'Ezer, the Tur connotes that it is not Midas Chasidus. Rather, he explains that the Gemara permits someone married, i.e. only if his wife is with him at the time, so he has Pas b'Salo (he can fulfill his desire when he wants). This is why the Gemara said 'if he was married', and not simply '(a) married (man is) permitted.' Surely, we do not permit permanently because he was once married a long time ago! The Gemara connotes that it was a Chidush that Rav Yehudah was married. I.e. the Chidush is that his wife was available. If so, we must be stringent about what is considered 'with his wife' for the Heter to apply. Sometimes a man separates from his wife for a long or short time. Therefore, the Tur was stringent, like he was stringent about the other answers. E.g. he was stringent about fear, for we do not know how much fear is needed. The Tur and R. Yonah are stringent based on letter of the law. It is not a mere Midas Chasidus.

Kaf ha'Chayim (43): The Acharonim hold like the Beis Yosef.

Beis Yosef (DH v'Ika): Why did the Tur and Rambam omit the Heter to help through the Beitzim below? They relied on what they wrote that one must be careful not to hold the Amah (Ever). This connotes that one may help through the Beitzim, for they are not called 'Amah'. Even though Shmuel told Rav Yehudah to hold the Amah, and one answer holds that he meant the Beitzim, Shmuel was not precise. He relied on Rav Yehudah, who knew that one may not hold the Ever, and it is permitted only through the Beitzim. Why did they omit the Heter due to fear? We are not experts to know how much fear inhibits Hirhur. It varies according to the height of the roof and the person's nature. Some people are easily frightened, and some are not afraid at all. Also, the Gemara gave other answers. It is not clear that we permit due to fear. This is why the Rosh did not make this distinction.

Question: If so, why may we rule like the other answers? Perhaps the Heter is not due to them, rather, due to fear!

Answer (Beis Yosef): The other answers were teachings of Amora'im. They were not said merely in order to answer the question from Shmuel. However, Semak permits (also) when there is fear.

Magen Avraham (14): If his wife is not there or she is Nidah, it is forbidden. Tosfos says that Rebbi was stringent, for he was married. He understands that 'below the belt' means touching the Ever. In Even ha'Ezer, the Shulchan Aruch rules like the Rambam. In YD 184:5, he rules that fear inhibits blood. He did not say that we are not experts about how much fear is needed! We must say that we are lenient about Vestos, which are mid'Rabanan. Zera l'Vatalah is a severe sin.

Kaf ha'Chayim (42): The Beis Shmuel (EH 23:4) permits even if his wife is not there or she is Nidah. Most Meforshim disagree.

Mishnah Berurah (25): If a married man is in a place where he fears falling, he need not be stringent at all.

Shulchan Aruch (EH 23:4): One may not hold the Ever while urinating. If he was married, it is permitted.

Beis Shmuel (4): This connotes that a married man is permitted even if his wife is not with him.

Gra (11): The Rif and Rosh brought all three answers. This connotes that they do not argue, like the Mechaber wrote in OC 3:14,15. The Rambam holds that the latter answers permit even a married man only in cases like Rav Yehudah, who was surely married. Even so, Shmuel permitted only (through the Beitzim or below the crown). The Rambam explains like Rav Nachman, that a married man is always permitted, and a bachelor is always forbidden. This is why he omitted the Heter of the Beitzim (and) below the crown, and cited the words of the Gemara, like he is wont to do. Since the Gemara did not explicitly permit or forbid the Beitzim or below the crown, the Rambam omitted this, like he often does.

Shulchan Aruch (ibid.): In every case he should never put his hand to his Ever, except when he needs to eliminate. See Orach Chayim 3.

Gra (12): The Mishnah says that if a man puts his hand to his Ever, it is worthy to be cut off. This connotes even if he is married. Below the navel is permitted, as long as he does not touch the Ever. We learn from Rebbi. The Shulchan Aruch rules like R. Eliezer, for the Sugya is like him. We asked from his opinion, and gave many answers. Also Rav Nachman, who permits a married man, discusses the above cases. The Gemara asked from R. Eliezer also in Shabbos 41a, Nidah 16b, Berachos 40a and Yoma 30a. See Tosfos there (DH Mitzvah) and in Nidah (13a DH Ochez).