In a little-publicised deal, Pepsi, Cola has ...... the entire soft drink market in Afghanistan.

In a little-publicised deal, Pepsi, Cola has captured the entire soft drink market in Afghanistan.
In this context, "captured" is the most appropriate verb to describe Pepsi, Cola's dominance or control over the entire soft drink market in Afghanistan. "Captured" implies gaining control or possession of something, which accurately conveys the idea of Pepsi, Cola's significant market share. Therefore, "captured" is the correct choice to complete the sentence.