I started using the long head of triceps branch to anterior division of the axillary nerve in around 2006 as described by Somsak Leechavengvongs. I quickly changed to using the medial head of triceps as a donor and have used this since 2008 to great effect. ~the latter has been popularised by Susan Mac`kinnon, however the rationale is not well described.
The medial head has a similar axon count to the long head. The medial head is longer allowing versatility in anastomosis site and avoids the need for release the the inferior teres major tendon which is needed in around 1.3 of long head branch cases due to insufficient donor nerve length and tension at the co-aptation site.
The medial head allows transfer closer to the muscle. The medial head has two branches and with intrneural neurolysis a single branch can be used ion cases where an augmentation nerve transfer is required or the full medial branch when there is a complete paralysis and no expected recovery of the axillary nerve. One branch can be sutured to the anterior division of the axillary nerve and pone to the posterior division of the axillary nerve after removal of the cutaneous upper lateral cutaneous nerve.
The final reason why I prefer to use the medial head rather than the long head as a donor is in cases where there is a C5 injury with loss of supraspinbatus or isolated axillary nerve injury with a supraspinatus cuff tear. In such cases there is a complete loss of muscle function to hold the head of the humerus in the glenoid fossa and the humeral head sublimes inferiorly. Activation of the long head of triceps relocates the shoulder and therefore I believe that the long head must not be denervated. The medial triceps is therefore more acceptable as a potential donor nerve.