How is absolute monarchy power transferred?

It passes from reigning monarch to legitimate heir when the reigning monarch dies or abdicates. The specifics of what defines a legitimate heir depends on the absolute monarchy. In some monarchies, the family member must be male -- but in others it can be female. In some monarchies, it must be a child of the current monarch -- but in others it can be a sibling. In some monarchies, if there is no immediate family, a new royal family is sought -- but in others, a more distant family member is sought.