Over the years, I have developed many theories about Santa.
Allfather Christmas- Santa is clearly the modern job of Odin One-Eye. He knows all, taking especial notice of valor ; he rides his slay with his eight-legged Sleipnir, distributing proper retribution.
This theory has a lot of history behind it, and of course would make a great graphic (yes, I have drawn pictures. Next year, there will be cards.). It works down to the numerology. Odin would of course have the endless budget required by Santa, coming from his magic reproducing ring. Odin even has known trade agreements with elves! And of course the decorated holiday tree had a historical Norse connection.
The only flaw in this theory is that it's kind of utterly terrifying. He's pretty much a reaper god, after all. The idea that children of especial courage may be carried off to Valhalla sort of changes the feel of the day.
That, and I can't figure out where the Valkyrie fit in.
God of Late December- Santa is a loa, able to possess the hearts and bodies of those who appeal to him with the proper offerings (cookies and milk, with lots of red and tinsel decoration). This explains why he looks like your parents; he IS, but he's Santa too. Like Baron Samedi.
I got nothing to prove this wrong, either. Except of course for the problem of him being way more lenient than most gods. But it would explain why parents never ever seem to have enough energy on Christmas day.
Elder God of the Dark Nights- Santa is an extradimensional being, equally present in all times and places visible to humans. Belief and hope provide a thin spot in thew barrier between worlds that allow him to manifest occasionally, increasing his fame and the number of people with the necessary belief. Seemingly benign, he induces a state of dangerous selflessness in the human mind, making people ultimately willing to share anything, including perhaps organs.
Problem, of course, is that he's way too nice to be associated with anything Lovecraft ever handled.
There is of course a heretical theory which suggests Santa simply doesn't exist. But people say that about fairies too, and if they don't exist, who keeps hiding my pens? Ergo.
What's your theory?