This follows typical CSS structures. Ideally you should place all of the critical CSS in the child.
This child should then be responsible for its defualt structure and style.
The parent may or may not choose to change that components CSS. It depends on the context.
For example:
A button component has its default styling, this will be things like size, colour ect.
I use this button component in my 'page' component. However in this case I was it positioned fixed, so my parent component will do this as this is styling in in the context of this components layout structure.
Hope that helps