Partial CNAME setup and sub, subdomains, using a subdomain

We’re trying to figure out if we can setup Cloudflare for an account with the partial CNAME setup. Something we have done before: https://developers.cloudflare.com/dns/zone-setups/partial-setup/setup/

What is different this time is there are sub, sub domains involved. We previously have not encountered this type of issue and I was unable to find clear answers elsewhere.

So to illustrate this request… the domain we want to use for the partial CNAME setup is something like:

subdomain.mycooldomain.com

What will happen to the domains that sit underneath that, such as:

one.subdomain.mycooldomain.com
two.subdomain.mycooldomain.com
three.subdomain.mycooldomain.com
etc…,

Do they stay under control of the authoritative DNS provider or will they go through Cloudflare after we would do the partial CNAME setup?