They've now got fed up with their host/designer (same package) who doesn't deliver what they promised
The client moves on obviously wants to take their domain name with them but it's registered in the hosts name.
My understanding is that if you can prove that it your name (letterheads, business stationery etc...) there's no argument
What if any is the advice here? regarding getting this name back to its "rightful" owner
Suzy
If the domain is registered to the host, the registration certificate and forms will most likely have been sent to the hosts - the client will need to get in touch and request that the domain be reregistered to themselves using these forms.
If the host isn't forthcoming, repeat the process and keep copies of the correspondence. After a fortnight has passed, the client should simply get in touch with Nominet and explain the situation.
Nominet will want to see copies of the documentation the client has sent to the host, along with any original invoices for the domain itself - they will explain the requirements to the client.
As mentioned, keep copies of everything and be civil to the existing hosts - the incorrect registration may have been a genuine mistake and if the client is civil, they are more likely to get the issue resolved quickly. If the problem does need referring to Nominet though, expect the process to take around four weeks to completion.
R.