When is it okay to reassign a ticket to another team?
A ticket should be owned by the team that is responsible for the service that is the focus of the ticket. For a request, this will be the service being requested, or at least some aspect of that service, and for an incident it is the service that is impaired in some way. Therefore, the purpose of reassigning a ticket is to get it to the right team – that is, the team responsible for the relevant service. Ideally, the relevant service will be recognised when the ticket is first created and the ticket will be assigned to the team named as the support team. Sometimes though, the true service is not immediately evident so the wrong one might be selected and the ticket assigned to an incorrect team. In this case, the dispatcher of that wrong team should select the correct service and team if they are known, or reassign the ticket back to ServiceLine if not known.

What to do if a ticket is owned by one team but assistance is needed from another team?
Whilst it is tempting simply to reassign the ticket to the team from which the help is needed, this is not appropriate as the owning team needs to keep control of the ticket. Instead, a task should be created from the ticket and that task assigned to the other team. Often that will mean that work on ticket has to wait for the task to be completed so if the user is agreeable, the ticket may be put on hold for a period that is acceptable to the user.

If a ticket or a task is reassigned to another team, should it also be assigned to a member of that team?
A ticket or task should never be assigned to an individual when it is assigned to a different team unless that person is expecting the ticket or task and this will most likely be the result of a prior conversation with the person.

Further details can be found in UoS-iSolutions-IcM004-I Incident Management and Request Fulfilment Best Practice, and in particular sections 2.3, 4.1 and 5.1.4.