I have a very small sample size (2 children
). Our son is a lefty, and has favored his left hand almost from when he first started reaching for things; family members, even friends and strangers would comment, "wow, he's a lefty already!" by the time he was 6 months old, and it never seemes to be in question, he 99.9% of the time went with his left hand. He's 5 now. DH's mom and brother are lefty, and his sister is virtually ambidextrous (DH is kind of ambi he does a few things as well or better lefty but most righty), so we weren't surprised at having a lefty, but were surprised at how soon he showed an almost exclusive preference. DD took a little longer to show favor, but by the time she was 1 it was pretty clear she favored her right hand, and uses her right almost exclusively at this point.
FWIW, as a baby/toddler, we'd always put things down in the middle for him and let him decide how to pick them up, we never encouraged either hand (because we knew there were other lefties in the family and didn't want to influence him - it was a conscious decision we made), so maybe that's part of the reason - maybe righties who don't have lefties in the family already kind of subconsciously tend to hand thigns to the right? Or something? Not that I think it's a bad thing, just a potential observation.