Hi all
This is not strictly speaking "a study" of mating nuc size but it certainly reflects a deep understanding of the issues:

Mating Nuclei.

Many are the opinions on the question of the size of nuclei for queen rearing apiaries. Some, among whom famous American Breeders, favour the baby nucleus, weak in bees, even as few as 500 of the latter. ...  In regard to the size of mating nuclei I do not wish you to think that I am advocating the other extreme. A full size hive is neither necessary nor advisable, and as you may like to know what I use, I will give the leading particulars of our nucleus hives which have been in use for many years.  

The hives are constructed for four frames 10 ½” x 10 ½” (outside dimensions) with a population which varies between 9 and 12 oz. of bees. Some queen rearers will say that this is nothing but a waste of bees and material but I hope to prove that it is justified.  Firstly, apart from the fact that never in my experience has such a nucleus ever abandoned its hive, a nucleus of this size is more than self supporting and I obtain at least one full frame of honey during the flowering of the Robinia (pseudo-acacia) weighing 4 ½ lbs. from each nucleus.  Secondly, I am convinced that the young queen acquires greater strength, is better developed and has her powers of reproduction increased when she is surrounded by respectable number of bees, than if compelled to pass her period of virginity and her early motherhood, both of which are periods of development, in a poor weak colony barely capable of doing more than exist with some help from outside.  

Thirdly, a frame 10 ½” x 10 ½”  is sufficiently large to enable bees to winter on. We keep a sufficient number of hives to take twelve of these frames, and in the autumn the nuclei are united in pairs under the better queen of the two and winter out of doors. The doubled nuclei not only winter safely, but they build up quickly of their own accord, so that by March they are well populated and in efficient condition. The queens are usually of August and September rearing, and when they are good ones the results in the early spring are really surprising.  

A. Zanini (General Manager) (1919) Italian Queens, Bee World, 1:10-12, 202-204

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