In my very limited experience? None. They just trust the company they acquired to have filtered you properly. They do ask for references (like academic records and so on) but that was about it.

Without discussing too many details, I believe the issue with Google's recruiting process is it was designed when the company was smaller and it follows the philosophy that anyone that goes through the hiring process should be ready to be thrown into any of the many Google projects and be able to function immediately. That's not strictly true anymore.

You have some divisions that are extremely hardcore or require very good knowledge of a particular field (think Google Cloud Platform vs. Android Kernel vs. Chrome vs. Search, all completely disparate projects), but there's also work for people that don't need to hold a PhD from MIT (think front-end development.)