The Father Connection

Does the father connection mean anything?
1. Jack went to Australia to claim father's body.
2. Kate on the run for killing her father.
3. Sawyer went to Australia looking for the man responsible for father's death.
4.Sun and Jin - escaping Sun's father.
5.Locke- Even though his back story isn't finished I'm sure the reason he is paralysed has to do with his father hence his need for the trip to prove himself. Plus I am sure the money his father left him funded the trip.
6. Claire- Mother of a fatherless child. Also MAY be Jack's sister.
7. Michael - Went to Australia to fulfill fatherly duties
8. Walt - Leaving Australia to go home with his father.
9.Echo - is a priest or a "Father" was in Australia on church matters.
10.Anna Lucia - killed man responsible for the loss of her child. ended relationship with the father of that child (hinted in her flashbacks) and found a father figure in Jack's dad.
11. Charlie - (This one may be strecthing it) Went to Australia to visit his brother who was a new father

That leaves Sayid, Libby, Hurley (whose father is absent, and we still don't know why he was there exactly), Rose and Bernard. Plus there is the fact that Desmond is most likely there due to his girlfriend's father.
Theory by: Harper Pitt