The Analytic Group here at Toronto had a guest speaker, Ted Sider, who gave a paper on parthood, which you can find here:
It was interesting, although I found parts very difficult to follow, not having had a chance to read the paper before it was presented (alas, they did not provide the URL beforehand). In any case, I don't have much to say about the talk itself. It did start me thinking about a number of completely different issues in mereology, and one is that we should perhaps pay more attention to the part-subject relation than we do. We do pay quite a bit of attention to part-whole relations; but the part-subject relation seems to be different, or at least potentially. This can be seen in the case of temporal parts (assuming there are temporal parts). Suppose you have an object O with temporal parts t1, t2, t3, etc. Now when we are talking about O, we can be talking about two entirely different things. Some people mean the whole sum of t1, t2, t3, etc. This is O-as-whole. But we can also mean the thing that has t1, etc, as the subject of the parts rather than as the whole. For instance, let t1 be Brandon yesterday; let t2 be Brandon today; let t3 be Brandon tomorrow, etc. Now, I can either take the whole of Brandon (t1 + t2 +t3 etc.), or take Brandon as a subject (the one has temporal part t1 at t1, etc.). It can also be seen in the case of spatial parts. Talking about the subject-part relation, I am wherever any part of me is. But this is not true of the whole-part relation (the whole of me is not where my finger is, for instance). We could perhaps express it by distinguishing between the relation 'part of' and the relation 'part belonging to' (or something along those lines. So in thinking about parts and wholes, we should perhaps think in terms of a triad rather than a dyad: in terms of subjects-parts-wholes rather than just parts and wholes. I'm sure someone else must have suggested something like this; I'll have to look into the matter a bit more - I have only a rough acquaintance with analytic mereology. Any suggestions for further reading?