What's the drip rail seal called?

Dig it all out or it will keep cracking. Spray some primer, sealer or what ever you have on any bare metal spots. Lay a nice bead of seam sealer. Use a small brush or your finger with a glove on & some paint thinner to smooth it out.
Its on a painted roof! What a shame.....I think it cracked when they used the infra red dryer after painting it...20 years ago.