(NYTimes) - Three years into an acrimonious legal and public relations battle between pop singer Kesha and her longtime producer Dr. Luke, who was once one of the industry's most untouchable titans, the pair remain deeply, uncomfortably entwined not just in court, but in business.

On Friday, Kesha will release Rainbow, her first album since Warrior in 2012, chronicling, with an inspirational bent, her years of personal and professional turmoil on songs like Bastards, Let 'Em Talk and Learn To Let Go.

But she will do so under the same extensive recording and music publishing contracts with Dr. Luke (born Lukasz Gottwald) that existed before she claimed in a 2014 lawsuit that he had for years "sexually, physically, verbally and emotionally abused" her. (He has strongly denied the accusations and no criminal charges have been filed.) Though #FreeKesha became a cause célèbre - at its height, Taylor Swift said she would donate US$250,000 (S$340,736) to support the singer - and her comeback has been greeted by fans as a victory and a rebirth, it follows a string of legal defeats that prevented Kesha from releasing music outside of her deals with Dr. Luke.

While her own contract claims were largely rejected by the court or withdrawn, she continues to face a lawsuit for defamation and breach of contract from Dr. Luke, who argues that her campaign against him has caused his work to dry up. (Though he has contributed to 40 Billboard Top 10 hits in his career, he has not been credited on one since 2015.)

For the last year, as the cases wound slowly through the system, Kesha and companies closely affiliated with Dr. Luke have worked together on completing Rainbow. The album will be released by Kemosabe Records - a subsidiary of Sony Music started in 2012 as a joint venture with Dr. Luke - and RCA, another Sony label, with Dr. Luke still standing to profit off an artist he first signed more than a decade ago. Below is a breakdown of where things currently stand between the parties.

Will Kesha's success benefit Dr. Luke?

The short answer is yes - any commercial triumphs Kesha experiences with Rainbow are, on paper, a win for Dr. Luke as well, given the ongoing contracts that cover both her recorded music and her songwriting royalties (or publishing).

Why is the album coming out now?

On tour last summer, Kesha told fans: "I can't share my new music with you. Please bear with me and keep praying that soon that day will come." In court, lawyers for Sony and Dr. Luke had said that the companies were willing to facilitate recording sessions for the singer with other producers, but her team argued that Dr. Luke had effectively blocked Kesha from making and releasing music because of her allegations. "Dr. Luke promised me he would stall my career if I ever stood up for myself for any reason," she wrote in a 2015 affidavit. "He is doing just that." According to her collaborators, including Ricky Reed and Ben Folds, Kesha began recording demos of new songs on her own and, as the legal quagmire continued, eventually handed over 22 tracks in various states of completion to her labels. From there, executives at both Kemosabe and RCA helped to steer the album process, jointly approving producers; lawyers for Dr. Luke said Kesha was paid a "substantial recording advance", as stipulated in her contract, while Dr. Luke was still Kemosabe's chief executive.

"It was a collaborative process, just like the making of a typical album," said Christine Lepera, a lawyer for the producer, adding, "Everything proceeded with the full support of Luke." His team argues that this arrangement - with Dr. Luke working in an approval capacity, but not hands-on with the album - could have happened all along. "Nothing changed legally that allowed her to release this album," Lepera said. "Nobody was stopping her from doing this years earlier." While Kesha's contracts stipulate that Dr. Luke must produce at least six songs on any album she releases, he has forgone that requirement on Rainbow and will instead pursue the equivalent producer royalties in court.

Representatives for Kesha declined to comment for this report.

Is Kesha barred from mentioning Dr. Luke?

Lawyers for the producer say no. Kesha's promotion of her raw new music - including op-eds she has written for publications like Rolling Stone and Mic - has relied on not-so-veiled allusions to her oppressors without mentioning Dr. Luke explicitly. "This song is about coming to feel empathy for someone else even if they hurt you or scare you," she wrote of the single Praying in Lenny Letter.

Where do the lawsuits stand now?

Dr. Luke's allegations against Kesha, which include breach-of-contract claims and two claims for defamation, are still in the early phases of fact discovery, expert discovery and depositions, with a trial unlikely until 2018. She has appealed the dismissal of her own claims (infliction of emotional distress, gender-based hate crimes, employment discrimination), as well as her request for a preliminary injunction, which would have allowed her to release music apart from Sony and Dr. Luke; there has been little movement on either appeal.

In yet another tabloid-baiting subplot, lawyers for Dr. Luke are demanding a deposition from Lady Gaga, whom they say received defamatory text messages about the producer from Kesha. Lady Gaga has resisted, citing her demanding schedule, with a spokesman arguing that she is "at most an ancillary witness". (She is on tour promoting her most recent album, Joanne.) Barring any surprises, like a settlement or a third-party buyout of Kesha's contracts, the singer owes Dr. Luke two more albums after Rainbow.