I've been asked the question so many times that I've decided to make a section about it...
The idea came from Super Butoden II, a Dragonball Z super famicon game. Under the tournament mode, you get little Super Deformed animations of each of the characters. (^_^ They're so cute!) And so I decided to make a 'little adopt a character thingo', just for my 'little website'. (Hey! It was! ...back then.)
I used Paintbrush (the height of modern technology), and GIFcon to make the backgrounds, then animate them. And after they were up for a few weeks, I decided I needed a Goten adoption, so I just followed the style of the others, basic, pixellated and all the rest. After one or two attempts, I did... then I needed a Chibi Trunks. Then a 17 and 18 and Yamcha and...
^_^ I guess I never stopped.
I now use Photoshop 6 to draw each character, and Animation Shop 2 to animate them. I have 47 characters up for adoption, and over 1500 adoptees... And yes, I still get emails from people who can't find the Adoption form.
Oh, and some tips if you're planning to start your own Adoption agency: Use something original, neat and have plenty of choice. Make sure the instructions are pretty clear, because half the Dragonball fanworld seem to tALk LIkE thIS and go 'duh?' when they walk into trees.