Since the processes involving warranty are availability, capacity, service continuity and information security, what are the processes, if any, which are involved in utility?
ITIL Planning Protection and Optimization (PPO)
concerning the utility aspect - fit for purpose - there is a tight relationship with service strategy and service portfolio. You need to watch SOA ; )
For utility we're looking at the aspects of a service that meet the functional needs of the consumer. This means that there are elements of the 4 warranty processes you have mentioned, as well as a reliance on Business Relationship Management, Service Portfolio Management, Service Catalogue Management, Service Level Management, Change Management, and also Financial Management to a certain degree.
To be honest there are very few processes that don't have an influence on the utility aspect of a service.