Gandalf's words seem to indicate the splintering of the blade was intentional.
Quote:
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'They tried to pierce your heart with a Morgul-knife which remains in the wound.
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Many Meetings (emphasis added)
The splinter working its way toward the heart slowly, causing a gradual fading effect, seems to have been the aim all along. Frodo would steadily lose his connection to the world of light, undergoing whatever physical and spirtual changes were necessary. I would think a stab to the heart would have caused simple death.
As for the WK's aiming for a specific part of Frodo, it doesn't seem he would have been trying for the neck. Frodo was throwing himself toward the ground when he was stabbed, so the intended point of penetration would need to be
lower than where Frodo actually obtained his wound, in his shoulder.