From the Super Mario Wiki
An Autograph is an item in Paper Mario, Paper Mario: The Thousand-Year Door, and Super Paper Mario. The signatures are of Luigi and Merluvlee in Paper Mario, the Excess Express engineer in Paper Mario: The Thousand-Year Door, and Merlumina in Super Paper Mario. In Paper Mario, the elderly Koopa Koot wants two Autographs and will reward Mario with three Star Pieces for Merluvlee's and only one coin for Luigi's.
In Paper Mario: The Thousand-Year Door, the Bob-omb boy on the Excess Express, Bub, wants to be a engineer when he grows up and requests Mario to get the engineer's autograph. When Mario brings it back to Bub, the young Bob-omb gives him a Shine Sprite.
In Super Paper Mario, old man Old Man Watchitt tells the player that a spirit has been haunting him lately and he now wants her autograph, giving Mario a piece of paper to have signed. When Mario gets to the temple Merlumina's spirit rests, she autographs the paper after she finishes pouring her heart out to him and telling Mario that she cannot sleep. Once he returns with the signed paper, Watchitt rewards the player with the You-Know-What, which is necessary in the long process of getting Piccolo, an optional Pixl in the game.