What was the result of a letter Count Bezukhov wrote before he died?

About a year before he dies, Count Kirill Bezukhov writes a letter to the Tsar asking if he can adopt his favorite illegitimate child, Pierre. The Count wants to leave all his property to Pierre, but as Pierre's illegitimate he won't be able to inherit. Hence the need to have him formally adopted.
The Tsar's permission allows the Count to change the details of his will, and so he's able to leave his entire estate to Pierre as planned. But Prince Vassily Kuragin's none too happy about the new arrangement. A relative of Count Bezukhov, he'd been expecting to inherit his estate, but now his dreams of phenomenal wealth have been thwarted by the change in the Count's will. But Vassily's nothing if not determined—as well as devious, self-serving, and greedy—and spends most of the novel trying to con Pierre out of the money and property he believes is rightfully his.