Question Create component like UI Image that respects the RectTransform size?

How do I create a custom component that behaves like UI image, where the size of the image is based on the RectTransform's size?

Right now I'm doing something simple with a SpriteRenderer to figure this out. In the UI Image, the size of the RectTransform changes the image size without modifying the scale. I want to do the same thing: I want my SpriteRenderer to somehow render at the size of the RectTransform.

I'm thinking a child game object with a scale would work, and then some how I connect the size to the scale. I'm unsure about this, since it feels like it might be overkill, and also since I don't know how to respond to size changes.