Complex sentence: Opposite the anterior superior spine of the ilium it gives off a large ascending branch, which ascends between the internal oblique and transversus abdominis muscles, supplying them, and anastomosing with the lumbar arteries and inferior epigastric artery.
Split into simpler sentences: Opposite the anterior superior iliac spine of the ilium, it gives off a large ascending branch. This branch ascends between the internal oblique muscle and the transversus abdominis muscle, supplying them, and anastomosing with the lumbar arteries and inferior epigastric artery.