Tosfos (Kiddushin 2b) writes that the term "kiddushin" in the context of marriage means that a wife is designated as being permitted only to her husband, just as an item of "hekdesh" is designated for the use only of the Beis haMikdash.
What if a person uses the term of "kiddushin" to refer to an object? Can a person say, "This talis is mekudeshes for me," meaning designated only for that individual's use? Tosfos says not. Designating a wife to be one's partner precludes her having a relationship with any one else (b'mah she'meyuchedes li hi ne'eseres...). The same cannot be said with respect to an object.
Why not? What does Tosfos mean? If a talis is lying in the street, anyone can take it. If I designate it as my talis and acquire it, this creates a prohibition of gezel which precludes anyone else from taking it. Why does the term kiddushin work with respect to a wife but not with respect to the talis -- in both cases other parties are precluded from having access?
Maybe I'll update with my thoughts later, but first I'll give you a chance to think it over.