Emirates Qantas Air NZ
Hi, we fly Emirates, Qantas and Air NZ a lot with small children. Also lots of other airlines. I can't say that I have ever had extra special treatment with small children but then I have never assumed that it was the role of the staff to look after my kids so I am pretty self sufficient. 15 years I have had at least one small kid on long haul flights at least 4 times a year and shorter trips about 4 times.
Emirates have always had amazing kids packs, with blankets with a soft toy with long arms that velcros around it and a soft nylon zip lunch box full of snacks, a Dr Zuess book and drink. You get to take it all with you. Before the blankets we used to get puppets and soft toys which was a bear you could dress up in national costumes that were from all the countries Emirates flew to.
On occassion Emirates have taken polaroids of the kids in their seats as a present. They have small kid sized ear phones so that they don't slip of their heads. The crew are very kind to the children and they have their own children oriented Frequent Flyer program, skysurfers.
Just flew Air NZ up to LAX from AKL last week and used the new skycouch configuration. This is useful for a family with young children you can make the seats into a small bed by raising the footrests and there are charging ports for universal adapters to keep your own equipment powered up to amuse the small ones. Sometimes a familiar game or movie is better than what is available on the plane screen. The bed is not large and you pay for the extra seat, about $NZ 699 for the AKL / LAX sector one way. You get extra pillows, two adults really couldn't lie down, but terrific for one adult and 2 small children, much much better than just an extra seat as there is the extra width. If you already have 3 seats booked and want the sky couch area in the plane you have to pay about $200 I think. It isn't free. Air NZ did get the children to hand out the sweets at the end of the flight.
Air NZ have some good in flight entertainment on the new 777-400 in economy. If flying trans tasman it isn't full service so you get the seat and pay for the rest and it isn't really a flight that requires interaction of staff with children as it is only 4 hours long. Emirates have probably the best inflight entertainment in the sky with hundreds of channels and lots and lots and lots of Disney movies. Often on long haul flights there isn't enough content that is age appropriate for say a 4 year old to stay engaged in it. Maybe one or two shows which is why I say that Emireates inflight rocks.
Qantas used to do nice kids backpacks but a lot of that has been scaled down in recent years and I haven't been flying them long haul.
As you do your thesis you will need to make sure that information is current as a lot of airlines have cut handouts to everyone in all classes of the plane.
We flew aeroflot HKG to Moscow and kids got really cute backpacks in the airline colours. I don't remember what was in them though.
Sydney airport has some good play areas as does Hong Kong. Sydney has courtesy strollers as does Dubai. Not sure if these are airline or airport sponsored. Sometimes they have an airline on them Qantas or Emirates sometimes they seem to be just unclaimed strollers. : - )