This section is from the book "Anatomy Of The Arteries Of The Human Body", by John Hatch Power. Also available from Amazon: Anatomy of the Arteries of the Human Body, with the Descriptive Anatomy of the Heart.
The Internal Circumflexa Ilii Artery, smaller than the preceding, usually arises a little beneath, and sometimes opposite to it: immediately after its origin it pierces the junction of the fascia transversalis and fascia iliaca, crossing over a small pouch or depression which we may observe between the outer side of the external iliac artery and the lunated margin of the fasciae at their junction; it then takes a direction upwards, backwards, and outwards, corresponding, not to Poupart's ligament, as usually represented, but to a white line which marks the junction of the two fasciae: this line is a little above and behind Poupart's ligament. Having arrived near the anterior superior spine of the ilium, it terminates by dividing into two branches, one of which supplies the broad muscles of the abdomen, and anastomoses with the inferior intercostal and lumbar arteries ; the other continues in the direction of the trunk, and, having arrived at the anterior superior spine of the ilium, terminates in anastomosing with the superficial circumflexa ilii, the external circumflexa femoris, the glutaeal, and ilio-lumbar arteries.
The Circumflexa Ilii Vein comes from the external iliac, and usually crosses in front of, sometimes behind, the external iliac artery, to arrive at its destination in the external iliac vein.