To quote <PERSON> himself from the chapter entitled 'Robert Silverberg' in his autobiography, 'I, Asimov':
In 1988, <PERSON> had an idea. [...] why not find someone who would take my story "Nightfall," now forty-seven years old, keep the story essentially as written, but add a detailed beginning and a detailed ending to it. [..]
<PERSON> said that we could always arrange for me to have full approval of the final novel and even make changes if I felt it necessary. [...]
[...] I explained to <PERSON>] that I didn't want gratuitous sex, unnecessary violence, or vulgar language in the novel, and he agreed to that, indicating that he would be satisfied to let me have the final word on any matters under dispute. When I said "Delete!" it would be deleted, and when I said "Change!" it would be changed.
[...]
Eventually, I received the extended "Nightfall" manuscript from <PERSON>. 26
Despite everything, I had fearfully anticipated receiving something I couldn't endure [...]
I need have had no fears. <PERSON> did a wonderful job and I could almost believe I had written the whole thing myself. He remained absolutely faithful to the original story and I had very little to argue with.
In short, the central third of the novel is essentially all <PERSON>'s work: it's his original short story with only some very minor changes. The first third and the final third are all <PERSON> - but within <PERSON>'s guidelines, and with <PERSON>'s approval/veto.
As for the other two <PERSON>/<PERSON> collaborations, 'Child of Time' ('The Ugly Little Boy') and 'The Positronic Man' ('The Bicentennial Man'), we know that <PERSON> saw <PERSON>'s original outline for one of them:
<PERSON> has already outlined his version of "The Ugly Little Boy." I have seen that outline and approve it heartily.
<PERSON>'s autobiography ends in 1990, and he died in April 1992. 'The Child of Time' (based on 'The Ugly Little Boy') was published in 1991, so it's likely that <PERSON> saw (and approved) the final manuscript. 'The Positronic Man' was published in 1992; <PERSON> was sickening during 1991 and gave up writing about August 1991, but it's possible that he also the final manuscript of this book before it was published. 26