The last of the three hip throws in Nagenokata, tsurikomigoshi, is another bear to teach kids, partly because it is such a large-amplitude throw.
In my work with my kids on Nagenokata, I've been emphasizing the role of uke to the point of almost making the main purpose of the kata to demonstrate uke's ukemi skills. This does not relegate tori to the role of passive by-stander. It forces tori develop the ability to position and support uke properly so that uke can demonstrate the ukemi properly. So, tori is the spotter.
So, how does this idea apply to TKgoshi?
By this point in the kata, uke and tori are pretty familiar with the 3-push attack and the tsugiashi stepping. In the previous 3-pushes, tori adjusted his left hand (in kataguruma) and his right hand (in haraigoshi) during the middle of the 3-step attack. This time, tori adjusts his footwork right at the end, by sliding his forward foot sideways to right beside uke's right foot at the end of step 3. Then tori turns back in with his hips against uke's thighs and pushes up on the collar grip.
From here, uke is positioned to take a regular forward rolling breakfall ro airfall (albeit a slightly larger than usual one).
So, from uke's POV this is not really a unusual thing. From a uke-centric POV you can say that this technique is in the kata just to allow uke to demonstrate a slightly larger than usual forward roll. The interesting part of this kata movement is how tori/spotter adjusts his footwork to position uke for his fall.
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