Democrats argue that who paid for the research is irrelevant to the veracity of its claims, which they say should be thoroughly investigated. Yet some of the Democrats who funded the dossier have been wary of being associated with it. The lead Perkins Coie lawyer representing both the campaign and the D.N.C., Marc Elias, pushed back earlier this year when asked whether his firm was the client for the dossier, whether he possessed it before the election and whether he was involved in efforts to encourage media outlets to write about its contents.

In October, the veteran Democratic consultant Anita Dunn, who is working with Perkins Coie, explained Mr. Elias’s earlier response. “Obviously, he was not at liberty to confirm Perkins Coie as the client at that point, and should perhaps have ‘no commented’ more artfully,” Ms. Dunn wrote in an email.

Is this sort of research common or legal?

Campaigns and party committees frequently pay companies to assemble what’s known in politics as opposition research — essentially damaging information about their opponents — and nothing is illegal about the practice.

However, Republicans and campaign watchdogs have accused the Clinton campaign and the D.N.C. of violating campaign finance laws by disguising the payments to Fusion GPS on mandatory disclosures to the Federal Election Commission. Their disclosure reports do not list any payments from the Clinton campaign or the D.N.C. to Fusion GPS. They do list a total of $12.4 million in payments to Perkins Coie, but that’s almost entirely for legal consulting, with only one payment — of $66,500 — for “research consulting” from the D.N.C.

In a complaint filed with the election commission in October, the Campaign Legal Center, a nonprofit group that urges stricter enforcement of election laws, alleged that “at least some of those payments were earmarked for Fusion GPS, with the purpose of conducting opposition research on Donald Trump.” The complaint asserts that the failure to list the ultimate purpose of that money “undermined the vital public information role that reporting is intended to serve.”

Graham M. Wilson, a partner at Perkins Coie, called the complaint “patently baseless,” in part because, he said, the research was done “to support the provision of legal services, and payments made by vendors to sub-vendors are not required to be disclosed in circumstances like this.”

Who else knew about the Fusion GPS research during the campaign?

Officials from the Clinton campaign and the D.N.C. have said they were unaware that Perkins Coie facilitated the research on their behalf, even though the law firm was using their money to pay for it. Even Mrs. Clinton found about Mr. Steele’s research only after BuzzFeed published the dossier, according to two associates who discussed the matter with her. They said that she was disappointed that the research — as well as the fact that the F.B.I. was looking into connections between Mr. Trump’s associates and Russia — was not made public before Election Day.