Dear Márcio,

I dont know if that stuff will be useful to illustrate that question. We have two examples: the first one from California and the next from Canada:

1. California's lieutenant governor is second in command in the state. The lieutenant governor assumes the role of governor if the governor is unable to perform his or her duties. The lieutenant governor also serves as the president of the state senate, regent of the University of California, and trustee of the California State University System. While some politicians describe the lieutenant governor's position as a thankless job that is constantly overshadowed by the governor, Bustamante has aimed to make the most of his position. He has not been content to just sit on state boards and commissions. Instead he has launched his own statewide initiatives, in addition to attending to his regular duties.

Fonte: http://biography.jrank.org/pages/3803/Bustamante-Cruz-M-1953-Lieutenant-Governor-Politician-Laid-Groundwork-During-First-Term.html

2. From Canada, we have an example at: http://www.lt.gov.on.ca/En/Role/Role_vice-royale.html