Daniels, whose real name is Stephanie Clifford, sued Trump and Cohen to get out of the "hush agreement" Cohen arranged just before the 2016 election to keep her quiet about her alleged tryst with Trump more than a decade ago.
Avenatti has been concerned that material seized in an Federal Bureau of Investigation raid on Cohen's office and home may include privileged documents and secretly recorded audio about his client, the adult-film star Stormy Daniels. "I want you to participate, or not be in the matter at all", Wood said.
Wood said at the hearing Wednesday that she had to balance the needs of lawyers for Cohen and Trump with the needs of criminal prosecutors.
The Journal reported Monday that Avenatti, who with Daniels has a California civil case filed against both President Trump and Cohen, was blocking prosecutors from obtaining documents and interviewing Davidson. He also pointed out the extensive publicity and harsh commentary made by Trump, as well as the president's own encounters in bankruptcy court.
Steven Ryan, Cohen's lead counsel, informed the choose "I would like extra time" and lobbied - unsuccessfully - for a mid-July deadline.
Matching Avenatti's flare for the dramatic, Ryan noted that he's never opposed a motion of this nature in his 37 years of practice, but he did so on Wednesday because of Avenatti's "intentional, malicious, and prejudicial release of information" which amounted to a "drive-by shooting" of his client.
Cohen did not speak during the hour-long hearing in Manhattan.
Avenatti, who's conducted a massive media blitz since taking Clifford's case, has previously been accused of appearing too often in the media and leveling attacks against Trump and Cohen. Ryan denied it, but said if his firm had released those audio tapes, "it would be the biggest story in America".
Of the material seized from Cohen's home, hotel and office in April, only two old Blackberry phones and the contents of a shredder have yet to be turned over to Cohen's lawyers, prosecutors said.
Upon leaving the courthouse in lower Manhattan, Cohen - who also has the Fox TV star Sean Hannity as a client - did not reply to a shouted question about whether he meant to cooperate with prosecutors. U.S. District Judge Kimba Wood told Avenatti he would need to file a formal application to join the case.
Avenatti did not elaborate on his decision in his motion to withdraw, noting that he could refile it "if necessary, at a later time", depending on what happens with Daniels' motion to intervene in the case.
"The relatively modest amount charged" by Jones, who is a partner at Bracewell, "confirms that there is very little privileged material for her to review and that her review is not a hard one", Riopelle said.
Avenatti gave a brief statement to reporters outside the courtroom once the hearing was finished, but focused on the documents that were the subject of the hearing in relation to attorney-client privilege, arguing that Cohen and his attorneys should release all audio recordings.
Barbara Jones, the special master reviewing the documents, wrote that more than 1.3 million documents provided to her so far were not marked as falling under attorney-client privilege.
Wood became involved after Cohen came to court, complaining that he feared attorney-client privilege would not be protected.