Family dependants who are not covered by marriage / partner status can generally join the UK resident family member, if that person is permanently settled in the UK. If there is a time limit on the resident who is in the UK, then usually the resident can only sponsor their children under the age of 18. They must be able to support and accommodate their dependants without recourse to public funds.
If you are a single parent based in the UK, you may need to show that you have always had sole responsibility for supporting your children.
Parents and Grandparents who are elderly and able to show that they have no other children to turn to for support and accommodation, may also apply to join you. They must be able to supply documentary evidence that they are fully dependant on you.