While answering and commenting on another question I discovered that I am apparently thinking about anonymity differently than everyone else who responded. There are two questions stemming from that discussion, this is the first:
What words can fill the gap in this sentence?
[Word] is anonymous.
The examples I seem to find acceptable:
The writer is anonymous.
The paper was anonymous.
The call was anonymous.
Should I be saying:
The paper was written anonymously.
The call was made anonymously.
All of your example sentences sound fine for me. In general, it’s acceptable to refer to a piece of communication as being anonymous if what you mean is that it was created anonymously. This is a common idiom.
However, this doesn’t necessarily apply to all words derived from the same stem. Saying the writer’s anonymity sounds fine; saying the paper’s anonymity strikes me as questionable. Others may find it to be unobjectionable, but I am among those speakers who would balk at the construction. Thus, for maximum clarity and fluency, you may find it useful to reword things like the paper’s anonymity to the anonymity of the paper’s author.