From Publishers Lunch:

The Other Side of the Larsson Dispute--And No Fourth Book

While there are number of issues of contention between the late Stieg Larsson's heirs (his father Erland and his brother Joakim) and his partner of thirty years Eva Gabrielsson, one matter has unfortunately been resolved. Joakim Larsson tells us "we have an agreement not to publish" the 200 pages of unfinished manuscript for a fourth book in The Girl... series. Eva Gedin, fiction publisher at Norstedts--which bought world rights to the first three books directly from the author--confirms her understanding that the Larssons and Gabrielsson "mutually decided that a fourth novel will not be published."

Joakim Larsson notes that he and his father have not been allowed to see the manuscript, which is in Gabrielsson's possession. By his account, Gabrielsson "wanted to make sure it was finished" but she also wanted to control the process, even though the family is control of the estate since the author died without leaving a formal will.

He also maintains that "we have not tried to gain access to any other [unfinished] material" of Stieg's. While Joakim still believes "the publishing house should decide" if the work could be completed, "I will not fight for it."

He does not believe that Gabrielsson will ever allow the family to see the manuscript, and presumes that the agreement not to publish is final.