We pick a.root-servers.net, one of the 13 root servers (1), and ask it about dorothyperkins.net and learn that net is delegated to 13 name servers (2), so we ask d.gtld-servers.net where we learn that dorothyperkins.net is delegated to two name servers, including bill.as13009.net (3), so we ask that one and get the following answer:
Dorothyperkins.net is a domain controlled by three domain name servers at as13009.net. All three of them are on different IP networks. Incoming mail for dorothyperkins.net is handled by four mail servers at caraway.co.uk. All four of them are on the same IP network.