In Office 365 for Small Businesses (P-plan), Microsoft offers the ability to configure your vanity domains for full DNS redelegation, which means Microsoft will host your DNS records for you on Microsoft public name servers.
When adding a new vanity domain to Office 365, you must first prove ownership of the domain name by creating a TXT or MX proof record at your domain registrar. Once that is complete, the vanity domain is shown as "Verified".
After verification is complete, there are more steps the domain registration wizard will walk you through, and one of those steps includes configuring full DNS redelegation. This is the step where Microsoft asks you to visit your domain registrar and point your vanity domain to use the Microsoft name servers for DNS.
In order for Microsoft to complete the redelegation of DNS, we must be able to verify that the name servers change has occurred. Once confirmation is complete, the vanity domain is stamped with a Capabilities value named "FullRedelegation".
If you are not sure whether some or all of your vanity domains have completed the setup process and are set for FullRegelegation, you can utilize some simple PowerShell to verify the status of each vanity domain in your Office 365 for Small Businesses tenant.
Get the script and read more here.