The competition for lordships is pretty simple. If you have a realm with as many regions as nobles, a density of 1, then there is no competition as everyone gets a lordship. If you have a realm with half as many regions as nobles, a density of 2, then only half the realm can have a lordship. The higher the density limit, the scarcer the lordships. The scarcer the lordships, the more likely there is competition for vacant lordships.
Dwilight was the main island I was thinking of as well.
