You can attach one component to another with:

public CUIComponent Append(CUIComponent child, string name = null)
public CUIComponent Prepend(CUIComponent child, string name = null)
public CUIComponent Insert(CUIComponent child, int index, string name = null)
ComponentA["some name"] = ComponentB
ComponentA.AddChildren = List<CUIComponent>

You can also set parent directly

ComponentB.Parent = ComponentA

But then you'll also need to manually add child to the parent children list

You can remove a child with

ComponentA.RemoveChild(ComponentB)

or by calling

ComponentB.RemoveSelf()

Or you can remove all children with

ComponentA.RemoveAllChildren()

Every component has a dictionary of NamedComponents
You can access it like this:

ComponentA["some name"]

this

ComponentA["some name"] = ComponentB

is the same as this

ComponentA.Append(ComponentB)
ComponentA.Remember(ComponentB, "some name")

if a child already has a parent it won't be added to the children list by "ComponentA["some name"]", it'll just be remembered

Also you can use Get(string name) method, it's like ComponentA["some name"] but it can give you nested component, and Get< T > version can also cast it for you

Header = Frame.Get<CUIHorizontalList>("layout.content.header");