Not getting results from the /uk-establishments end point

I am having a go at interrogating the /uk-establishments end point. I want to see how companies are related (parent/child relationships etc). I’ve tried many company numbers but I always get an empty array of items.
For example, I know Plusnet are owned by BT, so I tried them:
This gives me an empty items array:
{ "etag": "61df390c63e7a04d3f25b28be691787537a56c17", "items": [], "kind": "related-companies", "links": { "self": "/company/03279013" } }

My question is, am I doing this incorrectly of is this endpoint just not often used much and so not reliably populated with data?
Thanks very much.

I think it’s only used for overseas companies with an office in the uk:

Their company number will usually start with FC (foreign company) and the establishment will usually start with BR (branch)

uk-establishments is related to FC type companies that have overseas company details or uk establishment details
So for example companies like :-

Thanks very much. That explains it.

Is it possible to get parent/child links between companies from the Companies house API?
Or am I barking up the wrong tree?

It probably depends on the nature or context of that link. Some of this is only exposed through Persons of Significant Control (PSC) which was only introduced in 2016 or so. You can see that for your Plusnet example here: Persons with significant control

You can’t do a reverse look-up of this information through the API though, it’s designed to find statuary information about a specific company, rather than to answer queires about companies that meet a certain criteria, and querying it has a lot of limitations as a result. For the latter you might want to inverstigate the bulk data products (eg: Companies House for PSCs). Alternatively there are probably some third party products where they have compiled this kind of information.

Thanks Ash, most helpful, I will have a look into that.