The act of being overly obsessed with an artist/person/character/etc.
STalker + fAN = STAN
Eminem's song "Stan" embodied all the aspects of what it means to be a huge fanatic of a music artist, and the word has since been used to encompass all obsessive fan behavior.
My Xander love comes from my Buffy stanning.
I've been stanning Beyonce for so long I couldn't stop if I wanted to.