What is Scrooge and Tiny Tim's relationship at the end of the story in A Christmas Carol?

Scrooge became like a father to Tiny Tim, looking out for him and his family.

At the beginning of the story, Scrooge seems to scarcely know of Tiny Tim’s existence.  He makes little effort to get to know Bob Cratchit or his family.  To Scrooge he is just a clerk and an employee.  They spend their days separate and solitary.  It is not until Scrooge visits the Cratchit family with the Ghost of Christmas Present that he really pays attention to Cratchit’s plight, and realizes he has a crippled son.

Scrooge, who previously claimed that the poor were “surplus population” and if they died it was no big deal, seems drawn to Cratchit’s youngest son.  Tim is pious, gentle, and clearly crippled.  He is a target for sympathy if ever there was one, and he seems to melt Scrooge’s heart.

“Spirit,” said Scrooge, with an interest he had never felt before, “tell me if Tiny Tim will live.”

“I see a vacant seat,” replied the Ghost, “…If these shadows remain unaltered by the Future, the child will die.”

“No, no,” said Scrooge. “Oh, no, kind Spirit! say he will be spared.” (Stave Three)

Scrooge’s reaction is one of pity, and maybe some measure of guilt.  After all, he never took an interest in Cratchit’s family.  He never intervened to help them because he simply didn’t care.  Now that he knows them and has seen them, and realizes that they are good people, he is torn.  He pities them and feels a connection to them, through Bob.  He takes ownership over them and their situation.

It is no coincidence that the first thing Scrooge does when he wakes up Christmas morning is send the Cratchit family the biggest turkey he can find.  He wants to help Bob immediately, and not waste any time before putting a little extra meat in Tiny Tim’s belly.  Scrooge later tells Bob that he wants to discuss his affairs, and tells him he will raise his salary “endeavour to assist your struggling family” (Stave Five).

More importantly, Scrooge takes an interest in the Cratchits beyond money.  Particularly, he seems fond of Tiny Tim.

Scrooge was better than his word. He did it all, and infinitely more; and to Tiny Tim, who did NOT die, he was a second father. (Stave Five)

Since he doesn’t have much of a family, Scrooge adopts the Cratchits as his surrogate family.  He becomes a good friend to Bob and a kindly uncle to Tiny Tim.  He will make sure that the Cratchits never again know hunger, and Tiny Tim will not only live but thrive.  To Scrooge, this is the true meaning of Christmas.  He has come to realize that there is no surplus population.  Every life is precious.

In Tiny Tim, Dickens created a character that tugs at the readers’ heartstrings and puts a name and face to poverty.  How could Dickens’s readers walk past a beggar child on the street now, and not think of Tiny Tim and the fate he so narrowly missed?  Dickens personified the poor, and took them out of the shadows.  His legacy of making readers care about their fellow man lives on to this day.