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As of my understanding, after we register a domain as our property in ICANN via a local domain-register authorized by a local internet society branch (like ISOC UK for Great Britain), we need to point the domain-register's DNS servers to those of the hosting providers by their DNS names and by that we "link" the hosting provider to ICANN and use the ICANN domain to address our Website directory,

Hence, is it true to say that an hosting provider's DNS server is what links the entire hosting environment to ICANN?

Stephen's answer gives you all the details, but I think your misconception or slight changes of wording is related to something else, the "IANA root".

ICANN oversees the running of the system, and plays no operational part (which is a simplification, as they technically run some root nameservers, and are also the "registry" of .int, but this is tangential to your case).

ICANN has a direct contract with gTLD registries, but it still needs to manage a single hierarchy in which all TLDs fit in, because obviously there is a need of uniqueness. This is called the "IANA root". Because there have been multiple attempts in the past of people trying, for technical, political, philosophical, experiment, to define other roots, which would/could carry other TLDs.

This was called "alternate roots". They all failed for various reasons. Or at least the one trying to sell "new" TLDs, that would work only in the alternate root. There are still some alternate roots used for experiments, like the YETI Project

But the IANA root is described in RFC 2826: "IAB Technical Comment on the Unique DNS Root" which says in its summary:

The DNS name space is a hierarchical name space derived from a
single, globally unique root. This is a technical constraint
inherent in the design of the DNS. Therefore it is not technically
feasible for there to be more than one root in the public DNS.
That one root must be supported by a set of coordinated root
servers administered by a unique naming authority.

IANA was previously a specific service just maintaining this and other parameters for the IETF. After ICANN was built, IANA became a service inside ICANN. After latest ICANN evolutions, IANA is now more technically called "PTI" for "Public Technical Identifiers", see https://pti.icann.org/
It is a separate structure, in contract with ICANN, that manages the IANA functions.

ICANN is several layers removed from your hosting. There is a link, but isn't a direct link in any sense.

1. ICANN is an organization that oversees the domain name system. They allow other companies to operate top level domains. They run some of the DNS servers that point to the DNS servers of the top level domain operators.


2. The top level domain operator runs the name servers for a top level domain and allows domains to be sold under that top level domain. For example Verisign operates the .com top level domain.


3. Your domain registrar sells domains and can insert NS records for the top level domain. For example GoDaddy registers domains and can insert NS records for .com domains to Verisign. These NS records point to your DNS records at your DNS hosting company.


4. Your DNS host has the A and CNAME records that point to your web hosting company.


5. Your web hosting company runs a web server on an IP address that is specified in your DNS records at your DNS host.

Your web host and your DNS host may not even be the same company. It is very common to get DNS hosting bundled with web hosting. However, you can use DNS hosting from your domain registrar or from another company.

When somebody wants to get to your website using your domain name, ICANN isn't usually involved at all.

1. The web browser contacts a local DNS server to get the IP address.


2. The local DNS server looks it up from a parent DNS server and then caches it.


3. If no parent has it in the cache, the DNS servers for the top level domain are consulted to get the NS records for your DNS host.


4. Your DNS host returns the IP address and sends it back down this chain.


5. The only time that ICANN's DNS server would be queried, is if no caching DNS server had the records for the top level domain. This happens only for a very small percentage of DNS requests.

Most of the time, ICANN isn't directly involved in fulfilling requests to your website. Even when it is involved, it is involved only tangentially and through several other intermediaries.