Is there any evidence that Google has a shadow profile for people? I know that it was revealed that Facebook did/does and everyone assumed that Google probably does too but I don't think I've ever seen evidence that this is the case.

Disclosure: I work for Google, but I'm genuinely curious. I've seen no evidence of "shadow profiles" but it is a big company so I couldn't say for sure one way or another.

When they launched Wave there were reports of all kinds of chaos because people were automatically added. I don't remember if this was a case of "oh, you had this contact? We'll add them to your friends automatically." or those people crossed some classification threshold, but there were cases of stalkers and abusive exes being added without permission.

I think the chances that Google had some type of profiling system for non users is well above 80%.

I might be missing something, does FB allow you delete the data from your shadow profile if you don't have/create an account ?

Post-GDPR both companies will be required to. GDPR entitles European citizens to go dynamite fishing by sending companies requests to delete any data that is identifiable as being associated with that citizen.

You have to identify yourself to make the request, but the process should be self healing because they are then required to also delete the PII in your request to delete your PII (unless it's required for regulatory reasons, but this applies more to banks than google or facebook).

And before that we were already entitled to request that data, which FB "respectfully" dragged their heels over when people actually tried to use that right.