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Rambam Hilchas Shabbos (1,15-16) If two people do a melacha on shabbos either each one does half of it, one does the akira and the other the hanacha or they do the whole melacha together and one is able to do it by himself, they are both patur. If none are able to do it by themselves and they did the whole thing together, they are both chayev. If one is able to do it and the other is not, the one able is chayev and the other is patur.
שבת ד,א
Tosfas questions why is the one placing the bread in the oven on purpose is chayev misah when his admonishment is a safek as maybe he will remove it? Tosfas answers that we judge as it is now. Normally it will bake. The baking does not require any action any more.
The requirement of 4 amos to place to or remove from is required because usually a person places something on a sturdy place. Tosfas says a place is considered 4 amos.
שבת ה,א
The hand has a chashivus and considered 4 amos. Rashi in Kesuvas (31,2) says that this applies to the halacha that a person can acquire ownership within his 4 amos, so one gains ownership from what is placed in his hand.
The Baal Hamoar Shabbos 96 explains that beside the reason of halacha Moshe Mesinai it is also logical that carying 4 amos in public domain is chayev as the 4 amos acquires ownership so you carry from prive domain to a public domain.