Hosting provider
A hosting provider stores a website's files on its servers; when the site owner ignores you, removal requests go to the host.
Finding it
Through IP and DNS records. Services like Cloudflare can hide the real host; report to them first and they forward the notice.
When to contact
Copyright, personal data, fraud and unlawful content; with a clear court order hosts usually act fast.
Frequently asked questions
Will a host take down the whole site?
For serious repeat violations, yes; usually only the content first.