Guns has always existed as two units, "the band" (public thing) and the "legal band".
When Adler was fired in 1990, the band changed legally and legally. Think of a band as a corporation, with shares (shares of overall income, shares of publishing revenues etc). When Adler was dropped, a new legal Guns N' Roses was constituted where Axl, who already had 25%, probably received Adler's share of the legal band (Adler would sue in 1993 and 1996 due to this money issue). The new legal GN'R now constituted Axl, Slash, Izzy and Duff as legal partners. Then, Izzy quit; Izzy's share in the legal partnership in terms of royalties, publishing and operating income also likely went to Axl. However, when he left, Izzy secured an agreement that he would receive a percentage of all GN'R's earnings (live shows, memorabilia, etc) until November 1997.
After Izzy left, a new legal partnership had to be drawn up. This happened in 1992 and codified Axl, Slash and Duff as the only legal members of Guns N' Roses. Gilby, Matt, and Dizzy, while members onstage, were salaried employees, not "partners". Monetarily, this new split left Axl, Slash and Duff as equal partners in the business aspect of Guns, but with Axl as majority shareholder so to speak. Included in this new partnership agreement was a clause which stated that if Axl were to be fired from Guns N' Roses, or quit, the legal name Guns N' Roses and such would belong solely to him.
Axl invoked this clause in December 1995 and resigned from the existing GN'R partnership, and created a new operating legal entity also called Guns N' Roses in which he was sole partner and shareholder. In this new partnership, Axl would get a percentage of all things Guns, and any new "members" would receive a set salary and contract.
It is likely, considering that Axl, Slash and Duff are getting percentages of the live shows (rather than Axl getting a percentage and then dolling it out in salary as with nuguns), the old GN'R partnership created in 1992 (which never ended, hence how Slash and Duff were able to battle Axl with regard to using GN'R music in films etc) has been reinstated, with Axl as majority shareholder but all three as equal partners in the business.
I could pull a wall of bullshit speculation out of my ass too, if that's what I was looking for. If you have a source for Axl buying out Steven's and Izzy's shares, or why it would make sense to give Axl all of Izzy's and Steven's shares, I will definitely look it over.
Not sure if this helps, but this is Axl basically saying (in his mygner Interview from years ago) that he had the rights to the name but Slash (And Duff) still had the rights to play the songs as long as they didn't use the G N' R name.
Q: Since you own the name, does it bother you at all when you see or hear things like "Slash of GUNS N' ROSES" and that he's still well recognized as one of the faces of the band?
Axl: "It doesn't bother me unless it's being done at my expense and or to keep him associated as in Guitar Hero. Him being [in] Guitar Hero's fine but not when Activison is using 'Jungle', having Yahoo! use 'Sweet Child' unauthorized, claims no involvement with Slash, his or anyone's image or VR or anyone or anyone's music in either camp in promotion or commercials etc. I wasn't broadsided. I read about it as it moved along but Activision continually denied it right up to the release. That's some lowlife chicanery on all their parts.
"Yes, Slash was in GUNS and on 'Jungle' (and the whole 'I came to him for his riff' is as much crap as him saying he brought 'Locomotive' and 'Coma' in as complete songs) and he has rights to perform it but not to be represented in this context in association with GUNS. And since they weren't granted the license, it'll take some sorting."
Q: Does Geffen or Universal have any rights over the name, or is it soley yours? For example they released the "Greatest Hits" under the GN'R name, so I was a bit confused over exactly how much the name belongs to the label, if at all.
Axl: "Universal has GUNS under contract but I own the name."
Q: How do/did you feel about VELVET REVOLVER playing GN'R songs live? Did you worry about them mucking up the songs or decreasing their value by playing them? Are you glad the former members still play those songs so regularly on stage? I seen SLASH'S SNAKEPIT live in July 1995 and they started playing instrumental "Paradise City" for the first two minutes before Slash stopped it by jokingly saying something like, "We better stop so we don't get sued!"
Axl: "I don't have problems with whoever doing the songs but film or video gets into sync rights and I don't have an interest in anyone new, old or whatever trying to sell themselves as GN'R under another name that way."
So it's pretty clear that Slash and Duff (at least) retained some rights to the songs. Adler and Izzy weren't mentioned at all during the interview, which would make one believe that neither was involved much in reference to rights/shares of the band or music....but that's 100% a guess.
Here is an excerpt from a legal textbook regarding "How to run your band's business" where the author uses Adler's removal from the band as an example. Basically saying that Adler gave up his legal share of the band (under duress) but eventually settled in court, giving up his rights/partnership for $2.5 million.
Another thing to note...that in all their court cases over song rights, etc....it was always Slash and Duff filing in court vs Axl....Izzy and Adler were never mentioned in most of those cases (Only time Adler was mentioned was in his own case). So reading between the lines would again, lead one to assume that any legal partenship was in terms of shares/rights to the songs/band were between Axl, Slash and Duff.
We now know Adler signed his shares/rights away with his court agreement. Other than Izzy not being involved in lawsuits, not much is known about his situation....but an educated guess would make one believe he must have settled at one point or another,