For much of the past decade, the Democratic Socialist Republic of Sri Lanka was more or less a family business — one that happened to be run on an island just 22 miles off the coast of the second-largest country in the world and astride a key shipping lane to the largest. By one estimate, former Sri Lankan President Mahinda Rajapaksa and his two high-ranking brothers controlled up to 70 percent of the nation’s budget, while 29 members of their extended family held senior positions in the government, civil service or industry.