According to the first Lashon the Chatzer of a Ketanah is Koneh her Get, however with regards to a Metzi'ah it is a Machlokes between Reish Lakish and R. Yochanan if her Chatzer is Koneh.
According to the second Lashon everyone agrees that the Chatzer of a Ketanah is Koneh her Metzi'ah, while regarding the Chatzer of a Katan it is a Machlokes between Reish Lakish and R. Yochanan. (1)
If someone sees a person running after a lame deer or a young bird that can't fly and he says my field shall be Zocheh for me he is Zocheh. (2)
If the deer is running normally or the birds can fly normally and he says that my field shall be Zocheh he is not Koneh.
A person is not Koneh with a Kinyan Chatzer if the Chatzer is not guarded unless he is standing next to the courtyard.
If a person remembers that he has bundles and then he leaves them for his workers and the workers forget them if he is still in the field it is not Shichechah, but if he is in the city it is Shichechah. (3)
If someone is harvesting a furrow and he forgets to harvest some of the produce if he forgets behind him it is Shichechah if he forgets in front of him it is not Shichechah.
Tovas Hana'ah (the benefit one has to get Terumah and Ma'aser to any Kohen that he chooses) is not Mamon.
The Torah states Nesinah regarding Terumah and Ma'aser and therefore they may not be given to the Kohen by way of Chalipin because Chalipin is not regarded as a Nesinah.
Terumah and Ma'aser may be given with a Kinyan Agav because a Kinyan Agav is regarded as a Nesinah.
R. Papa says that if someone is Koneh Hefker with a Kinyan Chatzer he must be standing next to his Chatzer but if he is Koneh a gift from his friend he is Koneh with his Chatzer even though he is not standing next to the Chatzer.
If a Get is placed in the property of a woman she is only divorced if she is standing next to her house or her Chatzer.
A Get may be given to a woman against her will.
A BIT MORE
1. According to the third Lashon there is no Machlokes between Reish Lakish and R. Yochanan; Reish Lakish was referring to a Metzi'ah when he said that the Chatzer of a Ketanah is not Koneh while R. Yochanan is referring to a Get when he said that he Chatzer is Koneh.
2. If he can run after them and reach them before they exit the Chatzer he is Koneh with a Kinyan Chatzer.
3. If he is still in the field it is not Shichechah unless he forgot them himself because otherwise his Chatzer is Koneh the bundles for him when his workers forget it.
KINYAN FOUR AMOS
If someone sees a person running after a lame deer or young birds that can't fly and he says my field shall be Zocheh for me he is Zocheh. The Magid Mishnah states that even though a person is Koneh with his four Amos even if he doesn't say anything that is because the Kinyan of four Amos is a stronger Kinyan than a Kinyan Chatzer because the person can reach down and take the object. The Beis Yosef answers that since the Rabanan instituted the Kinyan of four Amos in order to prevent fights they didn't want to differentiate between whether he said anything or not because if so there will still be fights. However, Tosfos says that the Mishnah is Lav Davka and even with a Kinyan Chatzer it is not necessary to say anything. (Tosfos Yom Tov)
If the owner of the field was in the city and he says that I know that my workers forgot bundles in a certain place it is Shichechah. If he was in the field and he says the same thing it is not Shichechah because in the field only Shichechah from the beginning is Shichechah but in the city even if he remembers and than he forgets it is Shichechah. (Rambam Hilchos Matnos Aniyim 6:9)