I'm drawing a tree for "the paw of the kitten" (from chapter 7 of Andrew Carnie's Syntax: A Generative Introduction). This chapter is "extending X-bar theory", so please keep that in mind when answering (i.e. please don't confuse me with too modern / alternative theories).
According to Carnie, a PP with "of" is usually a complement, and some tests would seem to confirm that in this case:
- Adjacent to head: *the paw which is white of the kitten (cf. [the paw of the kitten] which is white)
- No two "of"-phrases allowed: *the paw of the kitten of the dog (intended: the paw which is of both the kitten and the dog)
So that would give the first tree below.
However, on the other hand, if I try to apply some constituency tests I want to take "the paw" as a constituent:
- You can insert a pause at "the paw — of the kitten" but not "the — paw of the kitten"
- Conjunction of "paw of the kitten" fails: *the paw of the kitten and leg of the horse (should be: the leg)
- Stand-alone: "What is of the kitten? The paw", but you cannot have "paw of the kitten" stand alone
- Movement: "Of the kitten is the paw" is kind of OK, but you clearly cannot move "paw of the kitten"
So that would give the second tree below.
How do I decide between these two options? I don't think the PP can be a complement to the D, because the complement position is already taken by "paw".