At first, the name baby giant arborvitae appears to be somewhat of an oxymoron. However, there is a reasonable explanation for this name. A popular cultivar, known as the green giant arborvitae, comes from the same parent species as the baby giant arborvitae. These plants share a similar appearance, with the one exception being size. Although the baby giant arborvitae looks similar to the green giant arborvitae, it grows to be much smaller, hence the name baby.