Some are barely old enough to walk and talk, much less understand the stock market. But thanks to South Korea's tax laws, a growing number of children as young as 1 are sitting on shareholdings collectively worth millions of dollars.

These rich kids are increasingly appearing on stockholder registries as the aging tycoons who fueled South Korea's postwar industrialization shift their stakes to descendants to avoid inheritance taxes that can reach 50 percent, the second-highest rate among OECD countries. By gifting shares now instead of passing them on at death, wealthy South Korean families can legally cut their tax bills.

While similar tax-minimization strategies are common around the world, gifted shares in other countries are often managed through trusts until children reach adulthood. In South Korea, where trusts offer few tax advantages and some tycoons are wary of relying on trustees from outside the family, the preference is to gift shares directly.