The T-34 T or TT-34? filled the role of armoured recovery vehicle (ARV) or tyagach (tractor), as they appear to have been solely used for towing damaged tanks out of the battle zone*. The more complete role of battlefield recovery given to western ARVs was probably left to the few M3 lend-lease chasses that made it to Russia.
My reading of the use of these recovery tractors is that they were all initially hulls with the turrets removed, that were modified in the field to plate over the turret ring. Some had a simple wooden hatch, others one or two hatches. Stowage baskets were added on an ad-hoc basis until some sort of order imposed itself at the end of the war and later. I am suspicious of some of the pictures around showing superstructures, as I think they are postwar modifications.
Having said that, I should really have modelled these tyagach by converting some of my earliest acquisitions. Instead, I used newer Plastic Soldier Company models, raiding my spares bin for odds and ends. The results may not be entirely authentic, but the method is! As ever, they are recognisable for what they are meant to be.
*http://en.wikipedia.org/wiki/T-34_variants (this article is pretty useful for comparing T-34 variants)