Assigning of IP addresses.

Apart from the private IP address ranges, which anybody can use, addresses are assigned globally by an organisation called IANA (The Internet Assigned Names and Numbers Authority).
This organisation assigns blocks of IP addresses to companies, including ISP's.
It is up to each companies IT staff how they use the addresses given, whether they give fixed addresses to each device, or use a DHCP server to disseminate IP address information to each computer on a network. It goes without saying that the DHCP server must have a fixed IP address as it cannot assign one to itself, and that there
can only be one DHCP server on a particular network at a particular time otherwise confusion will reign.