I'm interested in knowing what percentage(a rough estimate) of admitted phd applicants in top-60 university have peer-reviewed papers.
I'm particular interested in theoretical computer science.
I don't have statistics on that particular number, but my anecdotal evidence is that most PhD students in my field (chemical engineering) have zero publication when they start, while a small (but nonnegligible) fraction has one paper.
However, you can gather such statistics yourself! Publications are, by definition, public... And you can sample admitted PhD students by looking at current PhD students. So, take a random sample of CV from PhD students in your field (from the web) and look for publications prior to PhD start in their publication list.
Having publications when you apply for graduate school is typically unusual. The reason is that it takes time to get something published (review process). What I have experienced is that students may have a publication in preparation based on their bachelor or masters work. It is rare that these are more than manuscripts by the time they apply for a PhD program (they get published during the first year, perhaps). It is only those who may have worked between their earlier degree and the time of their PhD application that may have something. It is, however, easy to see if that is the case (a year of work rather than going straight from one to the other) so it is easy to understand why someone has come a little further than someone else. I therefore doubt it has a major impact.
To widen the perspective: In the application process, the fact that someone's earlier degree might result in a paper can be covered in a personal reference/recommendation letter. Keep in mind that all studies done at a lower level may not be publishable (because of time constraints for the work). It is hence important to have someone evaluate your efforts since the quality of the research at lower levels may not necessarily be best judged by a publication alone and a good word is always taken seriously.
So published papers are rare and when they occur there is usually a clear reason for why this has been possible to achieve when moving from one stage to the next in the education.
While there might be reasons for wanting this data, I am not sure what it will tell you. There may be some data out there (I don't know where) that may show a correlation between the number of publications and the chances of getting admitted to a PhD program. While publications may correlate with admissions, I doubt that it is causative. The Phd admissions process is all about trying to assess the ability of an applicant to conduct research. A publication goes a long way towards demonstrating that ability, but there are many other ways (e.g., strong reference letters).