You may wonder what sorts of picture book I submitted to Oshima International Picture Book Competition in the past.
I illustrated a story based on myself; a girl seeks who she is and finds the answer in being an artist.
I wrote the story in English and translated it into Japanese. I put both Japanese and English in the picture book.
Here we go!
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Search for a Star
There once was a little girl who loved painting and drawing. One day, she left a country where cherry blossoms were beautiful and set off for a trip to discover who she was.
The girl jumped on a boat headed for unknown countries, woke up in sunrise on an open field, read many books at
stone buildings, sipped some beer at a pub, visited a red broken dream, listened to a wind on salt pads, looked up sunset and counted stars, and kept sketching anything amazed her all the time.
One day, the girl asked a wise lady, “Who am I?” The lady said, “You already know the answer. Within you are so many answers. They are waiting to be realized, " gently smiling at the girl and her drawings. 
“I am me. No more, no less.” The girl looked back her journey and realized what she had most loved.
“I'm the artist!” the girl found the answer. The world always
kindly awaited her and unfolded its beauty. Now, wind, color, light, moment, everything the girl wants to catch on paper with her hands.
Today, the grown-up girl knows she's settled down in
Country of Art where people have universal language and can unite together for peace and love. Beyond time, space, race, religion, culture, war, anything.
The girl happily enjoys drawing and painting...forever and ever. 
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The entry condition for the competition is "all handmade." You make a story and pictures. Then, make them into a book all by yourself. You may try a "pop-up" book or a "usual book style". I chose the usual binded book. Your idea makes a unique and wonderful picture book! Binding papers is tricky. My friend illustrator Tony Flowers used a sketch book. But for me, a sketch book was not helpful, because papers did not hold watercolors well. So, I used both sides
of Arche watercolour papers and bound them in a folder.
The Ohsima picture book museum was really kind and sent me the visitors's comments on my picture book.
Oshima International Picture Book Competition is getting popular. More and more participants join it.
Another international picture book competition that sounds interesting is
"Aozora International Picture Book Competition"
run by ANA, a Japanese Airline company.
2010 competition is already closed.
Even though a bit old, you can get a big picture of the entry conditions here.
http://www.ana.co.jp/eng/aboutana/ehonvol05/
They said, "A competition for picture books is designed to illustrate the importance of "the environment." First prize worth 200,000 yen. "
ANA 'Aozora' Competition PO Box 48 Ota-Ku
Kamata Post Office Tokyo
Email: kankyou@ana.co.jp
Hopefully, they do not change the conditions too much. Check new information later or in a next year.
Wish you good luck, everybody!!
Cheers!

Oshima International Picture Book Competition and Aozora International Picture Book Competition