Delete or remove of domain can only be done once they expire. Once a domain is registered successfully, it remains active until its expiration date.
The domain will be removed from your Z.com account after expiration and deleted sometime after the grace period (usually around 30 days).
You may leave the domain until it expires if you no longer want to use it. However, ensure that you have off the auto-renew function so the domain will not automatically renew, nearing its expiration date.