Sporadic shut down, what could it be?
My MacBook Pro, either identical or nearly so, suddenly failed in precisely the same manner. Before finding Michael's comments I performed similar troubleshoothing, including battery removal, with the same results - even with the battery disconnected the sudden abrupt shutdowns persist.
I'm essentially certain my battery's in good condition and there is no history of liquid spills or other contamination events of any kind.
It seems clear that this is an internal hardware failure of some kind. I've already alternately swapped the SODIMMs, confirming that they're not related to the failure.
Next I'll disconnect the hard and optical drives, then confirm that the abrupt shut downs persist. If so I'll look at voltage rails, starting at the external power converter's mag safe connector. Due to the strikingly abrupt nature of the shutdowns I suspect sudden overloads (or perhaps complete shorts) cause the external power converter to shut down in protection mode.
If so I'll look for an intermittent component.