The children follow /use/share their father's surname.

are the same with their fathers 应该是are the same as that of their father's The children follow /use/share their father's surname.

a child takes his father's surname a child bears his father's surname 在来个句子，可以更灵活的用： Traditionally, the father's family name is the first choice for a... Chinese kid's surname, although the use of the mother's name is not uncommon. 从传统来看，孩子一般随爸爸姓，尽管也不乏跟妈妈姓的情况。