In my experience, you really only see Integer Explorer in China.
That being said, locally modified versions of Internet Explorer are extremely common. I can't remember their names off the top of my head, but even relatively unsophisticated users frequently download alternative versions of IE, which are generally based off of older IEs. (At least last time I was living there, which was about 16 months ago, so take this with a grain of salt)
Web designers / developers aren't focused on standards in the same way they are in the US/Europe, so other browsers may not display pages as expected. The Chinese Internet is quickly catching up with the rest of the world's in terms of quality, but it still lags behind.
Also, a significant chunk of the population primarily uses computers in Web Cafes rather than at home, so they don't even have the option of installing other browsers.
I know that in Korea, IE / Windows is basically the only choice, no one really registers the existence of anything else, so I presume it would be pretty similar in the rest of east Asia.
http://www.maylonggroup.com/M-150_MID.htm
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CPU ARM9(VM8505+)
Memory RAM 256MB DDR
Flash Built-in Flash
Display Touch Panel 7" TFT LCD
Resolution 800 X 480 Pixels
WIFI 802.11b/g
Input/Output
Touch Panel Resistive type touch panel
Speaker Built-in loud speakers
SD/MMC T-Flash card slot
Network/USB Dongle for RJ-45 network and USB connection
Buttons/Switches Power On/Off, Volume adjustment
Battery Built-in Li-Polymer battery
Charger Input AC 100-240V, 0.5A
Output 9V, 1500MA
Physical Characteristics Dimension 7.5" X 4.6" X 0.3"
Weight 12 OZ