When encountering Aveline and Wesley, choosing any answer yields Rivalry Carver: rivalry (+5).
Blackpowder Promise Rivalry Carver: rivalry (+5) if Hawke refuses to help Javaris.
Tranquility: Agree to help Anders because his friend is a mage Rivalry (+5)
Bait and Switch: Make It Worth My Time talking with Anso Rivalry (+5)
The Unbidden Rescue Rivalry Carver: rivalry (+5) if Hawke refuses to rescue Saemus Dumar. Rivalry Carver: rivalry (+5) if, upon returning Saemus to the Viscount, Hawke says Saemus went too far, or says they are both stubborn fools.
Wayward Son Rivalry Carver: rivalry (+10) if Hawke lets Feynriel go to the Dalish.
Family History Rivalry Carver: rivalry (+15) if Hawke chooses the aggressive/direct dialogue options.
Loose Ends Rivalry Carver: rivalry (+10) if Hawke agrees to help Athenril; or if the quest was obtained from Meeran, if Hawke completes the job and kills Lord Harrimann after the latter explains he convinced the Viscount to send aid to Ferelden.
The Deep Roads Expedition Rivalry Carver: rivalry (+10) if Hawke does not bring Carver along.
Enemies Among Us Rivalry Carver: rivalry (+5) if Hawke says "The Order needs to change" when talking to Knight-Captain Cullen after completing the quest.