As a general rule, it is the obligation of parents to keep and train their children till they become able doing their affairs. I was wondering if Islam has mentioned any specific age for it. For instance till the age Tamayyoz (التمییز) or puberty (البلوغ) or even more than it?
1- The Messenger (PBUH) said "Teach your kids to pray when they are 7 years and enforce it on them when they are 10 years.”
2- In another Hadith (Prophetic statement) he said "Play with your son for 7 years, discipline him for 7 years and take him as a friend for 7 years. Means between 14 and 21 according to the conditions. Some youth become independent before others. It is not the age in years but the employment and financial ability.
3- The female children are different and you take care of your daughter until she gets married. Concerning their marriage the messenger said. "If comes to you one who you accept his faith and his Morals (ethics, and Akhlaq), then accept him for marriage. If you do not do, then it will be severe tribulation and corruption in the Earth. Means Wealth, and family status, etc. should not be considered a barrier in accepting men for marriage.