Thirteen ‘Competitors to the Throne’ (nobles with a claim to the throne) asked Edward I to be considered as the future King of Scotland.
The Competitors' graphic below decribes the breakdown of the family tree.
Before Edward would decide, he demanded that all the Competitors accept him as their overlord, which they agreed to.
This agreement is known as the 'Award of Norham’ and effectively gave Edward ownership of Scotland. The Scottish nobles thought that this promise would be forgotten once a King was chosen.
In the end, only two of the Competitors had any serious claim to the throne - John Balliol and Robert Bruce.