1 : mysteriously and without human intervention
The problem resolved itself automagically.
2 : occurring or self-acting in an involuntary or spontaneous manner by seemingly supernatural or magical means
This computer has automagically rebooted.
The problem has automagically fixed itself.
Does he want me to just automagically figure this out?----Merriam-Webster's Open Dictionary
M-W's Open Dictionary is a feature on Merriam-Webster Online that allows word wits to submit found or invented neologisms, or, as the website puts it, "coinages and recent new-word discoveries."
According to its editor, "Open Dictionary now has received more than 7,000 submissions for all kinds of words, from slang to technical, playful to serious, and from fanciful coinages to words that may indeed find their way into regular dictionaries."--Merriam-Webster's Open Dictionary
If you are a logophile with arch appreciations for trick-witted jokes and smack-smart japes, visit the Open Dictionary and you'll be automagically delighted.--B'n' J'n.