In general the donor kidney is transplanted into the recipient's iliac fossa. The external iliac artery and vein are used as the recipeint's vascular supply. It is usually necessary to have a longer vein than artery on the donor kidney for two reasons, firstly the recipeint's iliac vein is deeper than the artery and secondly, when the kidney is placed into the iliac fossa the longer vein will nicely roll over the artery so that neither are under tension or risk kinking. The ureter is anastamosed directly to the bladder.
It is most convenient to place the left donor kidney in the right iliac fossa and the right donor kidney in the left iliac fossa. But this is not essential. The kidney is usually orientated so that the collecting system is anterior, this is to facilitate percutaneous cannulation of the collecting system should this be necessary in the post operative period.
It is wise to inspect the donor kidney prior to the recipient being anaesthetised.