The gemara concludes that a chatzer can either work as a "yad" or as a "shliach". There are many variables as to what may be needed for the chatzer to work: 1. zechus, not a chov. 2. a protected chatzer. 3. standing next to it. 4. da'as acheres being makneh the object.
These are the rules (as recorded in the Rosh):
To acquire a gett which can be given against her will, the chatzer cannot serve as a shli'ach only as a yad, therefore we require her to be standing next to the chatzer AND for it to be a protected area (chatzer mishtameres) which are both characteristics of a yad. Why is this true? Why can't a woman "appoint" the chatzer to serve as her shliach just as she can appoint a shliach to receive her gett? It seems that the chatzer which is inanimate object cannot be "appointed" as a shliach. In a case where it is clear to all that the receiver would want the chatzer to serve as a shliach (such as a matana or metziah where it is a zechus and therefore there is an "anan sahadi" that he wants it), it can be considered a shliach. But in a case where the receiver wouldn't always want it to serve as a shliach such as by a gett which is a chov, it can never be a shliach.
But to acquire a gift or lost object, the chatzer can either be functioning as a yad or a shliach, depending on the circumstances. When it is functioning as a shliach, the receiver doesn't have to be standing next to it, just as a live shliach can function as an agent in the absence of the owner. This is true so long as the chatzer is protected, but if the chatzer isn't protected, then he must either be standing there (to create a protected chatzer or work as a yad) or have a da'as acheres being makneh the object. Therefore, to acquire a lost object that does not have anyone being makneh it to him, it must be in a protected field, or he must be standing there (so it is considered protected or serves as a yad). Why does the chatzer have to be protected to serve as a shliach? The Rosh explains that one will generally only choose a shliach who is "protected" so that the object will be safe in his hand, therefore a chatzeir that is unprotected cannot serve as a shliach since we no longer have the "anan sahadi" that one will ALWAYS want it to be his shliach. [When the field isn't protected but he is standing there, the reason that it works is different for a man and woman - for a woman it works as a yad, but for a man chatzer cannot be a yad therefore it works as a shliach (since he can easily reach the objects it is like they are in his hand)].
BUT for a matana that has an advantage of da'as acheres being makneh it, the chatzer can serve as a shliach even if it is unprotected. Why does the da'as acheres compensate for the chatzer being protected? The Rosh explains:
אבל במתנה מסכמת דעת המקבל בכל מקום שיתנהו הנותן שיזכה לו המקום שיזכה לו המקום ושמירת הנותן חשובה לו כשמירתו The language of the Rosh is not so clear, but he seems to say that when there is a "giver", the receiver trusts the giver to protect the object and therefore the chatzer can serve as a shliach even though the field is not protected.