Question

What is a "domicile address" / "local presence" / "trustee service"? When to use it?

Answer

Domicile address (also referred to as "local presence" or "trustee services") implies the presence of a real address in the territory of the state under whose management the registry is located. Some registries, such as Afnic (.fr) and few others, require the owner to have a "local address" during registration. In some cases the address needs to be in the country itself or in the EU.
(Full requirements per tld are mentioned in the details TLD page)

If an owner don’t have such an address, it's possible to enable and activate this option during registration or transfer.

Finally, the user can be sure that the registration will complete successfully and there will be no problems throughout the lifecycle of the domain.

In case a local presence is required but a domicile service via Openprovider is not available, the registrant needs to have an address themselves, otherwise, registration is not possible.

Outgoing transfers and Transfer codes

When a trustee service is used for a domain, it is common that an external transfer code can not be requested. The provider will ask to first disable the trustee service, to update the domain to the trustee service of a new provider or to a new address which is eligible for that extension, before they allow the requesting of the external transfer code. The provider wants to prevent that their trustee is used for domains which are not under their management.