I get the impression that the success of Sam's part in the quest was due to a certain amount of blindness to the true dangers of the situation. He knew things were big and very scary but his love for his master may have helped to block out his understanding of the enormity of events around him. Being focussed on helping Frodo through everything confronting him would therefore take Sam's attention away from his own situation and in some way make it easier to be strong and carry on as the loyal servant. There is no doubt in my mind that all of Sam's actions are attributable to his love for Frodo.
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"It is plain indeed that in spite of later estrangement Hobbits are relatives of ours..."
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