Broken Capillaries are thread-like veins that result from dilation of blood capillaries. The veins are mostly apparent in people with dry, sensitive skin. Broken Capillaries are also known by other names like dilated capillaries, Spider Veins and Varicose Veins.They are observed in children as well as older people.The condition is more common in people who are about 30 years of age or older.roken Capillaries are also known by other names like dilated capillaries, Spider Veins and Varicose Veins. They are observed in children as well as older people. The condition is more common in people who are about 30 years of age or older.