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So I thankfully was extended an offer at a firm (T50-40ish) as a recent grad, "contingent" on passing a conflict check. First, any thoughts on how often entry-level associates are denied based on this?

Second, how do I go about this? I did a bunch of tiny, short term projects my first summer and then worked at a small firm. I worked on a bunch of projects at the firm, but they haven't been greatly responsive to my requests for even basic info on the projects I worked on (though I am very confident there would be no conflict between them and the hiring firm). The first summer gig was more helpful but they ultimately advised that I ask the conflict checkers at the hiring firm what they're looking for/whether the small projects are required, due to the burden of finding these short-term projects.

I guess, what is usually expected in these situations? The other concern is that I don't want to bother the hiring firm with questions since I don't want to annoy them.
Thanks

Bump.

Similar situation, as a first-time lateral though

They usually want a list of your former clients and any parties you were adverse to. To a lesser extent, a brief description of what you worked on and the approximate time that you worked on the matter is helpful. Just be smart about it and deliver the information in a coherent format.

I haven't seen entry-level associates denied based on conflicts. I've seen laterals get turned down on rare occasion (e.g., prospective employee was tangentially involved in ongoing litigation adverse to company X, and he wanted to work for an IP lit group that got a huge chunk of its work from company X).

I have literally never heard of any new associate failing a conflict check.

Some people had to sign waivers and what not but nobody “failed.”

OP, you're way overthinking this. Every firm job I know of includes a conflicts check, whether you're just starting out or lateraling. That means every one of the thousands of first year associates starting in any of the BL firms have gone through this process, with the vast majority of them having done some legal work for some clients during their first summers at the very least. This is pretty much a check the box activity. Don't stress the little stuff.