Damage assignment and lifelink

[Destore117]

Attacking creature has lifelink.
A creature blocks.
If a creatures toughness is lower than my creatures total power. Will I gain life equal to the blocking creatures toughness or equal to the total damage (my creatures power) dealt to the blocking creature?

For example say I had a {Trepenation blade} on a {Vampire Nighthawk} attack he gets pumped to 5/3 and my opponent blocks with a 2/1 {Vaporkin}
Would I gain 1 life or 5?

[MementoMori]

5.

119.2a: Damage may be dealt as a result of combat. Each attacking and blocking creature deals combat damage equal to its power during the combat damage step.

[Destore117]

Basically my creature deals it's total power to the blocking creature? And not just fatal damage right?

[MementoMori]

 Yes. Creatures always deal combat damage equal to their power, regardless of opposing creatures' power or the defending player's life total.

[Destore117]

Alright. Just wasn't sure if it would stop counting when the creature technically dies from 1 damage.

[Pleeb]

Big creatures aren't content to merely kill small creatures with the tenacity to block them. They want to grind their bones into the ground and rip the desiccated carcass to shreds.

Besides, you never know when that annoying {healing salve} will get played. Best to make sure.