Certification on Demand refers to a process where digital certificates are issued for a signature creation device that has already been sent out and is in the hands of the customer.

Heiko Rossnagel

Heiko Rossnagel from University Frankfurt, Chair of Mobile Business and Multilateral Security specifically mentioned Certification on Demand in connection with a mobile signature

Mobile signature

A mobile signature is a digital signature generated either on a mobile phone or on a SIM card.-Origins of the term:mSignThe term first appeared in articles introducing mSign . It was founded in 1999 and comprised 35 member companies...

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"The mobile operator could sell SIM-cards equipped with a key generator for one or
more key pair(s) which can be used for the signing functionality. After obtaining the
SIM-card from the mobile operator, the customer can then generate the keys and
activate the signature component and the public key(s) can be certified by any Certification
Service Provider on demand.
Through the separation of the telephone functionality and the (possibly later) certification
of the user’s identity by a certification service provider, both functions can be
sold separately and can be obtained from different providers.
The carrier will probably face increased costs for the signature capable SIM-card but
can also expect increasing traffic caused by signature services. All distribution channels
will remain unchanged."

Sources

http://www.wiiw.de/publikationen/MobileQualifiedElectronicSigna917.pdf