^ Well don't you know that within an hour of a Borg cube reaching the Death Star stationing itself on the other side away from the laser, It'd assimilate the entire structure? This estamate is conclusively determined via observation of the Star Trek episode Regeneration. Wherein the flagship Enterprise gets assimilated by Borg Technology. It only takes about a minute to assimilate the structure. Given an estamate that the CGI Enterprise is 10 football fields in area. We can conclude that ¼ of the Death Star should be assimilated within the first half-hour. Given the exponential rate of growth for Borg nano-tech. It stands to reason that the next sections should be overtaken within a ½ time as the preceeding section. Therefore 15 minutes later from previous ¼ takeover the Death Star should be ½ borg sphere. Consequently, 7.5 minutes later it should be a Borg Sphere.

(Seriously though, I'm just sleep deprived and, just making all this up. I'm likely completely wrong. I'de be suprised if I'm right.)