I think 托婴中心 is for 0-3 year-old babies, as same as 托儿所，they provide a special care and cultivate the ability of infants by trained service personnel; There is another place named 幼儿园，it's for 3-6 years old children, it provide a lot of interesting activities and some simple classes, such as math, music, painting and so on, and I think the most important thing is 幼儿园 fosters the ability of living independence, and helping each other; 安亲班，we don't say it this way, we call it 课后班 on mainland，is for 3-12 years old children. Many children's parents have to work everyday, and some of them have to work on weekends, so children go to 课后班 after school and go there on weekends if their parents don't have time to take care of them. Children can do homework and play together there, of course there are many trained teachers would guide children to finish their homework. Cheers