What is the proper punctuation of "your welcome"? Is it a shortened form of "you are welcome"?
It can be. "You're welcome" is a response to "thank you" and is a shortened form of "you are welcome". But there are situations where "your welcome" is correct.
Let's explore a couple of cases:
In the case where we have an exchange between two people being polite, such as:
Person 1: Thanks for the scone.
Person 2: You're welcome.
In this case, "you're welcome" is indeed a shortened form of "you are welcome".
However, you can also have a case where "your welcome" is correct - it would deal with someone commenting on or relating to someone else's welcome. For example:
Person 1: You were a delightful guest.
Person 2: Your welcome was the start of a wonderful stay.
In this case, "your welcome" is indicating that Person 1 went out of his way to make Person 2 feel special - and it started with Person 1's welcoming of Person 2.