Gemara

18b (Beraisa): All agree that one can sell (his daughter to be a slave, even if she is) a widow to a Kohen Gadol.

Question: How did she become a widow (while a minor)? If she was Mekadesh herself, she would not be called a widow (her Kidushin was void)!

44b (Shmuel (and Rav)): If a minor accepted Kidushin without her father's knowledge, she needs (before marrying someone else) a Get and Mi'un (annulment of a marriage mid'Rabanan).

(Rav Acha brei d'Rav Ika): She needs a Get, lest her father consented to the Kidushin. She needs Mi'un, lest her father did not consent to the Kidushin.

Mi'un makes people suspect that she is not Vadai Mekudeshes, so if Levi (who was Mekadesh her) is Mekadesh her sister, they will not ignore it.

(Rav Nachman): Shmuel's law applies only when there were Shiduchin (Levi already discussed with her father his intent to be Mekadesh her).

Version #1 (Ula): Even Mi'un is not needed.

Question: Does Ula say so even when there were Shiduchin?!

Answer: No. Ula did not comment on what Rav Nachman said.

Version #2 (Ula): If a minor became Mekudeshes without her father's knowledge, even Mi'un is not required.

45a (Ravina): Even those concerned lest a man consented to his daughter's Kidushin, are not concerned lest a man consented to his father's Kidushin.

Question: Perhaps the son told the father that he wanted to be Mekadesh her!

Answer (Rabah bar Simi): Really, Rav and Shmuel would be concerned. Ravina explicitly said that he does not hold like Rav and Shmuel.

45b: David and his wife Sarah argued about whom their daughter would marry. In the end, David agreed that she marry Sarah's relative. During the meal honoring the Kidushin to her relative, his relative was Mekadesh her in another room.

(Abaye): "Yisre'elim will not do unjustly or lie" (surely, David does not consent).

(Rava): One does not make a banquet for naught (if he consented, the Kidushin to her relative was Batel, and the meal was in vain).

If he did not exert himself to make the meal, Rava would be concerned lest he agreed, but Abaye would not.

Rishonim

Rif and Rosh (2:7): Shmuel says that if a minor accepted Kidushin without her father's knowledge, she needs a Get. Rav Nachman says that this is only if there were Shiduchin. Ula does not require even Mi'un. The Halachah does not follow Shmuel, for Ravina disagrees, and he is Basra. Even if a Na'arah was Mekadesh herself without her father's knowledge, even if he consented it is not Kidushin.

Rebuttal (Rosh 8): If he explicitly consented, all agree that she is Mekudeshes!

Rambam (Hilchos Ishus 3:13): If a girl before Bagrus accepted Kidushin without her father's knowledge, she is not Mekudeshes, even if he consented afterwards.

Rosh (2:6): The Halachah follows R. Yochanan, who says that all agree that a Na'arah with a father cannot be Mekadesh herself. We do not distinguish a Na'arah who was Mekadesh herself from a minor. We are not more concerned lest her father consented just because she has Da'as. Shmuel discusses a minor because Mi'un does not apply to a Na'arah. In several places, Chachamim required a Get for an adult, without concern lest people think that the 'husband' cannot be Mekadesh her sister. Perhaps for an adult we must announce that there was no Kidushin mid'Oraisa.

Ri'az (in Shiltei ha'Giborim 18b): If a minor accepted Kidushin without her father's knowledge, we are not concerned even if he consented when he heard, even if her father made Shiduchin. If she was a Na'arah and he consented, she is fully Mekudeshes, even if there were no Shiduchin. The Ri is stringent about a minor when there were Shiduchin. I am stringent whenever the father consented when he heard.

Rosh (7): On 18b, the Gemara said that if a minor was Mekadesh herself (and her husband died), she would not be called a widow. This is like Ravina. This is even if there were Shiduchin, and she did Nisu'in.

Poskim

Shulchan Aruch (EH 37:11): If a minor or Na'arah accepted Kidushin from Levi without her father's knowledge or had Nisu'in, this is nothing, even if her father made Shiduchin, and he explicitly consented afterwards.

Question (Bach DH u'Mah she'Chosav v'Afilu): If the father wanted to be Mekadesh her to Levi, we are concerned lest he accepted (Sa'if 12)! Rather, the text should say 'he made Shiduchin with the father', i.e. he sent to the father and asked him to be Mekadesh her to him.

Chelkas Mechokek (17, and Beis Shmuel 15 citing Rivash 193): We need not change the text. Her father wanted to himself receive the money from Levi!

Shulchan Aruch (ibid.): Some say that if he consented when he heard, she is Mekudeshes from when he heard, even without Shiduchin.

Gra (30): Tosfos explains that in the first version of Ula, Rav and Shmuel discussed without Shiduchin.

Beis Shmuel (19): There is no concern if he did not consent. Some are stringent about a Na'arah.

Shulchan Aruch (EH 37:12): If the father revealed that he intended to Mekadesh his minor daughter to Reuven and she took Kidushin from him, we are concerned lest the father consented.

Beis Yosef (DH u'Mah she'Chosav u'Ketanah): This is logical. However, the Ramah (brought in the Tur) adds that if the father toiled to arrange to Mekadesh her to someone else, we are not concerned. I disagree.

Chelkas Mechokek (23): The Shulchan Aruch omitted the Ramah's words because he disagrees. The Ramah learns from Rava (Kidushin 45b) that if one agreed to Kidushin that would make his toil (for a different Shiduch) futile, his agreement was insincere. Surely, one does not toil for nothing.

Beis Shmuel (24): If Levi asked David to be Meshadech Levi, and David was Mekadesh her to him, some say that she is Mekudeshes (EH 35:4). Here, the Shulchan Aruch says Stam that we are concerned. There, Levi did not make a Shali'ach. The Rosh holds that consent is as if he previously told her 'go receive your Kidushin', i.e. Shelichus. He holds that there, Levi did not express desire to be Mekadesh, but here her father did. Alternatively, here we are concerned because her father was present at the time of Kidushin.