Who runs the internet
Not a leaderboard. Concentration. That a handful of companies answer, route, front and vouch for most of the web is a systemic-risk fact, and it is only a fact if you say what you measured it against. So every lane below carries its own denominator, because we know the DNS provider for far more domains than we know the certificate issuer, and pretending otherwise would flatter the numbers.
A bounded slice, and it is not a random one. These lanes are recomputed from a capped walk of the catalog taken in alphabetical order: up to 300,000 domains of ~809,000. So every denominator below is what that walk could read, never the limit of what we hold, and because the walk is a prefix rather than a sample the shares are a bounded reading and not a survey of the internet. For the same question answered over the whole scanned corpus, see the state of the internet.
DNS
Who answers for the internet?
One provider covers half of it. The top 3 hold 98.1% of the 143,001 domains in this walk that carry a reading for it.
Who handles its mail? (a domain often uses several)
2 providers cover half of it. The top 3 hold 81.8% of the 99,936 domains in this walk that carry a reading for it.
CDN
Who sits in front of it?
One provider covers half of it. The top 3 hold 100.0% of the 116,524 domains in this walk that carry a reading for it.
Certificate authorities
Who vouches for its identity?
2 providers cover half of it. The top 3 hold 84.3% of the 248,754 domains in this walk that carry a reading for it.
Hosting networks
Whose machines is it actually on?
3 providers cover half of it. The top 3 hold 51.0% of the 227,541 domains in this walk that carry a reading for it.
How these shares are counted. A domain counts once per lane, and providers are collapsed to the company rather than the label ("Cloudflare (proxied)" and "Cloudflare" are the same company wearing two hats). A domain whose lane we could not observe is left out of that lane entirely rather than counted as a zero, because not knowing is not the same as nobody. Every figure comes from a signed observation you can re-verify.
The other half of this question. This page answers how much of the internet a provider holds. For which domains are newly observed on a provider and which ones left, see provider watch.