Is it possible to register a sub-domain if you don't own the base domain?For example, could I register NickLarsen.random.com if I don't own random.com?
DNS sub-domain registration
domains;subdomain
No.  This is not possible unless the owner of the domain allows it.As per Wikipedia:The Domain Name System distributes the  responsibility of assigning domain  names and mapping those names to IP  addresses by designating authoritative  name servers  for each domain.  Authoritative name servers are  assigned to be responsible for their  particular domains, and in turn can  assign other authoritative name  servers for their sub-domains.