if i set a custom provider for a

ComponentResource

, and inside the constructor of the CR I create a child resource but forget to add

{ parent: this }

, which provider does the child resource use?

It'll use your global default provider. You must use the parent option for it to become a child of the component resource

It is also limited by the allowed providers. Resources defined in a package will only use providers compatible with that package. Child resources from the aws package will only use an aws.Provider, etc.