M..
My daughter has done this too. We have gone to playgroups or the playground, and my daughter will run up to a total stranger and ask them to pick her up. Its usually another mom, and when the other mom picks her up, my daughter is quite content to let the other mom hold her. I used to get jealous too. My DD also gets tons of love and attention from us, so I don't think that is the problem. She is 27 months old now, and she is a very social little girl. She is not afraid of strangers at all, she is not shy at all. I think this behavior is just a sign that you daughter is going to be a social person. Try not to let it bother you. I know it definately makes a mommy jealous though!