TfL's "Free travel areas without Oyster adult accompanying map" shows a vast network in South London, including Richmond - Clapham Junction - Surbiton, labelled as "5-10 Zip Oyster photocard required to travel free". I'll leave it to the forum experts to decide whether this means that it's an area based Ticket, thus being valid for non-stop splits, or if it's just a PAYG card with a vast set of single fares charged at £0.00 (and thus is invalid if not touched in).
It's a complicated one because the 5-10 ZIP brings the discounted PAYG fare down to zero, but that's not quite the same thing as it being an area-based concessionary pass. It isn't a Travelcard.
If it's a PAYG ticket that brings the fare down to zero, does that mean that *stopping* splits are also not allowed unless the child taps in/out at the split?
I note that for example Gatwick Airport to London Bridge costs £7.55 peak on the 5-10 Zip Card, but Gatwick airport to East Croydon costs £3.30 while East Croydon to London Bridge is free. This split obviously requires tapping out at East Croydon to be charged the PAYG fare for the first leg, but a paper/barcode Child Anytime Day Single for Gatwick Airport to East Croydon costs £3.40 and avoids the need to tap at East Croydon - there will be an incomplete journey on the Oyster Card for tapping out at London Bridge only, but in practice this is charged at £0.00. So is a stopping split between a National Rail ticket and an un-tapped 5-10 Zip Oyster valid or not?
How did you not get charged for making an incomplete journey? An Oyster/contactless card cannot really be used for split ticketing as you need to alight, tap out, and enter with the ticket. It is easiest to just pay the extra money for a ticket from Clapham to be completely honest.
Travelcards loaded on Oyster cards do not charge for incomplete taps within the zone of validity of the Travelcard. (Without this, they wouldn't be combineable with Boundary Zone tickets.) I have observed the same behaviour for 5-10 Zip Oyster Cards. Freedom Passes and 60+ London Oyster cards do not hold a PAYG balance at all so cannot charge for incomplete journeys either.
We're talking about Zip 5-10 Oyster (and in my case 60+ Oyster) neither of which have any concept of payment.
5-10 Zip Oyster can hold a PAYG balance, for use e.g. to Gatwick (see the red lines on the map) or on the Cable Car. (But it can also be used without a PAYG balance for free travel where valid.)
A 5-10 Oyster is just a regular Oyster PAYG card with a concession as others have stated. It does not allow free travel on NR - that is only for TfL branded services. And in fact it does not even matter if you technically take the long way using only LO - you still get charged if you have not tapped out.
It does allow free travel on basically all NR lines within Zones 1-9 (see the blue lines on the map).
Bonus question: For the National Rail Lines with "Free travel [...] when accompanied by a fare-paying adult", such as Euston - Watford, can the child make a non-stop split between "no ticket" and a Watford - Milton Keynes ticket, in the company of an adult with a Euston - Milton Keynes ticket?