Yes, it happened... my beautiful bradford pear tree split.looks good on three sides but now I have a island with a damaged tree. Should I cut it down or just haul off the giant branch and leave it be?

Do you value it for its fruit, or its landscaping value? If it is fruit, you might even consider leaving the broken limb attached until after you can harvest the fruit. Then after it goes dormant, carefully cut it off leaving as neat of a wound as you can. The balance of the tree will heal and continue to yield fruit for many more years. The other branches and new growth will slowly fill in the gaps.

If it is a sore thumb in an attractive landscaped area, and you have not been doing the work to maintain good fruiting, perhaps you should cut it down and replace it. To some of us, our trees are old friends, with care, outliving us. Still, we lose some of them. The trees in our area have taken a beating recently. We had a major ice storm early this year, and later wind. The crews the power company hired did a very professional job, but others left the trees with a butchered look after topping.