The only question I have (and I don't have a strong opinion) is whether the first character of the prop should be capitalised or not?

We also have https://github.com/mui-org/material-ui/blob/3e4854b39b17511d9b312071ca93061eeb503f5d/packages/material-ui/src/Input/Input.js#L542.
We also have the xxxProps where xxx is capitalized based on the component name, e.g. InputProps and inputProps.

The only question I have (and I don't have a strong opinion) is whether the first character of the prop should be capitalised or not?

This is a compliment to the existing component property, which pertains to the root element. I feel like these props should follow a lowerCamelCase naming convention.

If this is the direction to go, the property name should remain capitalized:

1. to be consistent with cases such as inputProps vs InputProps
2. stops the destructuring aliasing needed such as

const { transitionComponent: TransitionComponent } = this.props
return <TransitionComponent/>

stops the destructuring aliasing needed such as...

This is a good point. Maybe we should go further and change component to Component for consistency and to eliminate the destructuring.

@kgregory The logics I have been following:

• destructuring aliasing wasn't a concern. It's better if we can avoid it, but I don't think it will matter in the long run if we execute on a versatile element customization story: support for component injection <XXXComponent />, render prop XXXrenderer() and element React.cloneElement(XXXnode)). Something we could fit into a single property name: all-inclusive.
• I like how the component suffix makes it obvious that it's a property to mess with the React structure. You don't need to go back to the property list API to see it.
• I have tried to follow a components?: Object structure like the classes. Ultimately, I reverted. The nesting wasn't providing me any additional value.
• The capitalization was added to stay consistent with the existing XXXProps properties. I don't have a strong feeling in either way. I have picked the solution requiring the less breaking changes possible.

@oliviertassinari You left out Snackbar.d.ts :-D
On it now.