Immigration (Visa, Entry Permission, and Related Matters) Regulations 2010, reg 20; INZ Operational Manual: Temporary Entry, E4.1
If you’re applying for a Visitor Visa, your application can also include your partner (whether of the same gender as you or a different gender) and your dependent children under 20, so that they don’t have to apply separately. You may also be able to include them if you’re applying for a Limited Visa.
But if you’re applying for a Work Visa or Student Visa, your partner and children will have to apply for the type of Temporary Visa that’s appropriate for what they want to do here. For example, if you’re applying for a Work Visa but your partner will just be visiting, they should apply separately for a Visitor Visa, and each of your school-age children should apply for a Student Visa so they can go to school here.