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What do you mean by stopping? If you mean the message "have stopped responding but have successfully recovered" then try re-installing the drivers for the graphics card and check your RAM timings and voltages are set correctly in the BIOS.
The 'choppiness' could be this?
http://en.wikipedia.org/wiki/Screen_tearing
Hope this helps.
issue is most likely the card not getting enough juice, try raising the voltage (if you can) or reducing the clocks.
could also be an issue with PSU not providing enough power
What graphics card have you got? I'l be suprised if it's the PSU, although it is a possibility.
Before you go checking wattages and changing your PSU over, get your ram timings set up correctly.
Please list the full spec of your machine.