Gemara

One cannot be Mekadesh another's property. "Ish Ki Yakdish Beiso Kodesh" teaches that one can be Makdish only things like his house, which are in his Reshus.

If Reuven tries to be Memir Shimon's Korban (transfer its Kedushah onto a Chulin animal), it takes effect only if Shimon authorized him to make Temurah on his Korban.

Chulin 139a - Question: A verse exempts Kodshim from Shilu'ach ha'Kan. What is the case?

Answer: He saw a Hefker nest and he was Makdish it.

Rejection: "Ish Ki Yakdish Beiso Kodesh" - one can be Makdish only things like his house, which he owns.

Nedarim 34b (Rava): An ownerless loaf was in front of Reuven. Reuven made it Hekdesh. If he later took it to eat it, he transgresses Me'ilah (benefiting from Hekdesh).

Me'ilah 13a (Mishnah): If one was Makdish an empty pit, waste heap, dovecote, tree or field, and they became full, Me'ilah applies to them but not to their contents;

R. Yosi says Me'ilah applies to a field and tree and to what later grows in them, for they grow from Hekdesh.

Bava Basra 79a (Beraisa): Me'ilah does not apply to what came later;

R. Elazar b'Rebbi Shimon says, Me'ilah applies to it.

(Rabah): They argue about a pit and dovecote. All agree that Me'ilah applies to what came later in a field and tree.

The first Tana holds like Chachamim, that one cannot be (Makdish or) Makneh (transfer ownership of) something that is not yet in the world;

R. Elazar b'Rebbi Shimon holds like R. Meir, that one can be Makneh something that is not yet in the world.

Bava Kama 115a (Mishnah): If Levi was carrying a barrel of wine, and Yehudah was carrying a jug of honey, and Yehudah's barrel cracked, and Levi spilled out his wine and saved the honey, he is paid only like a worker.

Question: The honey was going to be lost. It is like Hefker!

(Beraisa): If a man was carrying jugs of wine and oil, and saw that they were breaking, he may not make the wine and oil Terumah to exempt what he has in his house. If he did, it is invalid.

Rishonim

Rambam (Hilchos Terumos 4:2): One cannot tithe Peros that are not his without consent of the owner.

Or Some'ach: The Yerushalmi asked whether the problem is that it is another's Peros, or because it is not his. This affects one who was Mafkir his Peros after final processing. It tried to learn from the Mishnah about Terumas Hekdesh. R. Hoshaya said that the case is, he was Makdish Tevel. This shows that one can separate Terumah from Hekdesh. Even though it is not his, since it is not another person's, one can separate Terumah. Rav Idi rejected this. Perhaps the Gizbar is like the owner, unlike R. Yosi. I bring a proof from Me'ilah 13a. If one was Makdish an empty pit... and they became full, Me'ilah applies to them but not to their contents. R. Yosi argues only about a field and tree. Tosfos (13a DH Aval) says that we do not find that a Chatzer acquires for Hekdesh. This implies that the Gizbar is unlike the owner. If he were like the owner, a Chatzer would acquire for Hekdesh if he stands near it! There is no proof from R. Yehudah, for the Shitah Mekubetzes (79a DH Aval) says that really it is Hekdesh, but there is no Me'ilah because a man was not Makdish it. R. Yosi holds that even so there is Me'ilah. He must say that there is no Me'ilah regarding a pit because the water that enters does not become Hekdesh; the Gizbar is not like the owner.

Or Some'ach (DH u'Lfi): We can say that the Tana'im argue (Bava Basra 79b) argue about whether the Gizbar is like the owner. However, perhaps that Sugya holds that one may tithe what is not his, since it is not another's. Just like one can tithe Hefker, one can tithe Hekdesh. No one argues with R. Yosi. The Sugya did not want to say that R. Elazar (b'Rebbi Shimon) holds that the Gizbar is like the owner. Abaye (Kidushin 62b) listed Tana'im who hold that one can be Makneh something that is not yet in the world. Tosfos (79b DH v'Rebbi) asked why he omitted R. Elazar. I answer that Abaye holds that R. Elazar holds that the Gizbar is like the owner, so there is no source to say that he holds that one can be Makneh something that is not yet in the world. The Bavli could hold that one can tithe Hefker, and the Gizbar can tithe Hekdesh, just Abaye disagrees.

Or Some'ach: The Gemara (Kidushin 41b) learns Shelichus from Terumah. If one may separate Hefker to be Terumah, just regarding another's Peros one can tithe only with permission, Shelichus does not apply to. Only permission is needed. This is like we say about Temurah. If the owner gives permission to make Temurah, it is like Hefker. (However, perhaps Shelichus is needed for the Mitzvah of separating Terumah.) Surely in such a case one cannot make them Terumah on other Peros.

Tosfos (Yevamos 89b DH she'Hefker): Regarding one who separates Tamei Terumah on Tahor Peros, we cannot say that Chachamim made the Peros Hefker (to nullify his separation), for afterwards the Peros are his and he must fix them.

Or Some'ach: This Tosfos clearly holds that tithing from Hefker does not work. I did not see Poskim address this Safek. This is astounding. They omitted the Yerushalmi. We cannot learn from the Yerushalmi in Bikurim (1:2), which says that if Peros were stolen, the owner cannot tithe (even) before despair. If one cannot tithe his Peros if they are not in his Reshus, all the more so one cannot tithe what is not his, e.g. Hefker! However, perhaps stolen Peros are worse than Hefker, for the thief has a Kinyan in them, i.e. he can acquire through Shinuy, and he has liability and a Chiyuv to return them to the owner.

Rosh and Ran (Nedarim 34b DH Haysah and DH Amar): The loaf was within four Amos of him. Therefore, Hekdesh takes effect on it, for we say that the four Amos around a person acquire for him (Bava Metzi'a 10a).

Ran (ibid.): He never acquired the loaf. Since he did not say that he acquires it, and he said that it is Hekdesh, he shows that he wants only Hekdesh to acquire. This is like one who picks up a (Hefker) Metzi'ah in order to acquire for someone else. He himself does not acquire it. Since he never acquired it, he is not a Gizbar on it, therefore he transgresses Me'ilah when he picks it up to eat it.

Poskim

Shulchan Aruch (YD 331:25): One must tithe Min ha'Mukaf. If one has 50 Sa'im here and 50 Sa'im elsewhere, he may not make two Sa'im here Terumah on the Peros in both places. B'Di'eved it is Terumah, as long as what he makes Terumah is guarded. If one was carrying barrels of wine or oil, and they are breaking, if he declared them Terumah to exempt what he has in his house, Lo Amar Klum. It seems that nowadays that Terumah perishes, due to Tum'ah, it becomes Terumah.

Tif'eres Yisrael (Demai 7:2): Even though if one separated Terumah that will be lost, it is not Terumah, the case of Tamei Peros is different.

Tif'eres Yakov (on Mishnayos Demai 7, Tif'eres Yisrael Os 7, DH k'Bava Kama): The reason one cannot tithe on what will be lost is because it is like Hefker. If so, even nowadays one cannot do so! Tif'eres Yisrael's answer is not understandable.

Note: If it is a fine to say that it is not Terumah, surely there is no fine nowadays that in any case the Terumah must be burned due to Tum'ah!

Achiezer (2 YD 37:4): One must tithe his own Peros to exempt his own Peros. However, there is a difference. The Terumah must be his, and in his Reshus. We learn from "Ish Ki Yakdish Es Beiso." One can be Makdish or Makneh only something that is his and in his Reshus, just like his house, but not Hefker, unless it is within his four Amos, or he could acquire it (Nedarim 34b, Ran and Rosh). Also Chulin 139a shows this. No Haknah or Hekdesh is needed for the Peros being exempted. However, the Torah revealed that one cannot tithe on what is not his, i.e. when another owns them. One can tithe on Hefker, for no one (owns it and) dissents. The Yerushalmi concluded that one cannot tithe Hefker. However, one can tithe on Hefker. In Bava Metzi'a we require Shelichus for the Terumah, but not for what is exempted. For the latter, it suffices that the owner does not object.

Shi'urei R. Shmuel (Rozovsky, Bava Metzi'a 21b, 6): The Gemara said that when the wine will be lost, others can acquire from Hefker. Perhaps this is precise. Since it was (objectively) lost to the owner and to everyone (just someone exerted himself and succeeded to save it), it immediately became Hefker. Or, perhaps it is merely despair. The Gemara means that others may acquire it, just like one may acquire from Hefker. Some Acharonim say that when one despairs, the object remains his until someone else acquires it. If so, why can't he make it Terumah? This is difficult only for the Nesivos ha'Mishpat (262:3), who says that one can retract from despair. According to those who say that one cannot retract from despair (e.g. Terumas ha'Kri 262), even though it is still his object, since others can acquire it (and he cannot stop them), it is no better than something not in his Reshus. He cannot change its status. All agree that he cannot make it Terumah.

Shi'urei R. Shmuel (DH uvi'Terumas): The Terumas ha'Kri (262) gives a third explanation of the Sugya. We assess that the owner (willingly) makes it Hefker. If so, why didn't the Yerushalmi resolve that one cannot tithe Hefker? Indeed, from the Beraisa itself without the Sugya, we cannot resolve this, for perhaps the Halachah is that one cannot make Terumah something destined to be lost. However, the Gemara says that it is due to Hefker. Also according to the other explanations, we should derive that all the more so one cannot tithe Hefker! A Talmid answered that something lost from the owner and everyone is worse than Hefker, for it cannot become the property of Kohanim, since it is lost also from them.