Greg is probably right w/r/t who has the least "by hand" approach. Other candidates that come to mind would be Toyota, Nissan, and Honda, although I don't have firsthand knowledge of their production practices.
I've mostly worked in plants that are nearer the other end of the spectrum.
- Very large engines (say 200L total displacement and up) are often stall-built, where the parts are brought to the engine and a single person or a few people labor in the stall to put it all together. They'll use lifting tools, etc., because the parts are very big, but a person is making decisions about very many things in the course of assembly. There is never anyone checking tolerances on the assembly line - excluding extreme circumstances, all of the parts are within spec when they arrive on the line. Simultaneous torqing of bolts is very common, but a person is still positioning and commanding the tool. Ring gap positions are of negligible significance, but the rings have to be put on right-side-up. Subassembly of certain systems is done on separate assembly lines, but again in a very manual process (too expensive to buy robots for lower volume).
- Smaller engines, say 7-150L, commonly move down assembly lines where there are varying degrees of automation. I haven't the data to do the graph, but my suspicion is that within this size range the level of automation is largely a function of the production volume. A particular engine that I'm familiar with has piston/ring/liner subassembly done manually on a side line, while the heads are assembled from bare machined castings to the completed product without a single touch by a human. The heads are manually positioned on the engine and bolt torquing is simultaneous w/hand-guided tool.
When you ask "how much automation should be allowed in a hand-built engine" you seem to be implying that being "hand built" is desirable for some reason - I would suggest that the opposite is true from a quality standpoint, assuming the economics were a wash. In the end, as I mentioned above, economics dictate what will be "hand built" vs. "automated production" and the lower volume products suffer the quality penalty associated with hand building because it's still cheaper to fix a few of 'em than to buy robots to build them all correctly.