I want to enter this contest, but I don't want to get into legal problems.
If you create a picture on Adobe Illustrator does it mean it's yours and you own it?
Illustrator is just a tool. If you create a picture with a pencil, paintbrush, or airbrush is it yours and you own it?
For example, what if you draw a picture of the Coca Cola logo? Do you own it?
Do a Google for "derivitive works."
If you create a picture ...
I for one find the use of the word create quite clear and unambiguous here, meaning exactly what it means, hence no need for speculation. With this, and
... on Adobe Illustrator does it mean it's yours and you own it?
I for one understand the question to mean whether you have the full rights over the artwork you create (all by yourself), irrespective of your using this specific application to create it.
But now we have moved into the realm of short answers, which I believe are bound to end as amounting to the same as the long answer.