a. He tore off the page of the book on which I had written my name.
I'd assume that I had written my name on the page. Is that correct?
b. He tore off the first page of the book, on which I had written my name.
I think this sentence is ambiguous. One can't tell if I had written my name on the page or on the book. Is that correct?
c. He was petting that kitten of the cat that I had bought.
I think this would most likely mean I had bought the cat, but there is a slight possibility that I had bought the kitten (if the cat had been mentioned before). Is that correct?
We have 'of-possessives' in all cases and then a noun is being modified. The rule seems to be that the noun that is closest to the modifying phrase is the one that is being modified. I don't think the 'rule' (if indeed there is such a rule) applies in all cases. Hence the question. I think in some cases there might be ambiguity.