I think there's quite a fair few factors to consider that make a successful transplant with autos possible, it's by no means a dark art, just needs good observation and practice.
our situation is of course different to most, we like to start as many seeds as possible knowing that we will cull and disgard many along the way, also the fact that we have a lot of different rooms and areas we can house reject plants if they aren't pulled. But be it regular or feminised seeds we are working with it's very very rare that we complete the whole cycle in one container.
thesedays many have and prefer the option to plant a fem seed and let it do the business (with good care from you guys green thumbs of course) but in the past when I only had limited space, I did a couple of times start in big pots, adhering to the 'don't transplate autos mantra' but a few times I was hit with bad male/female ratios and it left me pretty boned...so from then I had to hedge my bets and start more than needed, wait for sex to be shown, cross fingers and transplant.
things I've found over the years.. Transplant too late = stunting, transplanting early = stunting, wrong container size = stunting.
Strain also plays a role too!
however, with a good environment, the correct sized starting container for the strain, a good technique and good timing, plants can be pretty much unaffected.
small solo cups/party cups .. I don't like, too small in my opinion
1.5 litre square pots, for an indica dominant auto, that shows sex at 2-2.5 weeks from sprout are ideal, nice and healthy growth above the surface, and you should have a lovely thick root mass below, water before transplant and really the por slips off like a charm without damaging any roots and it's seconds to do.
The material and thickness of the pot makes a difference to the ease, I prefer the slightly flexible plastic, too hard and thick and it's difficult to squeeze the pot and free it up.
However, you might think starting in a bigger size is beneficial to the transplant but, if the roots haven't really bound the substrate together then there's a danger it will fall apart. Messy and your plant won't like you as much.
with an auto that is known to be bigger or sexes closer to 3 weeks, I really like two litre Pop bottles modified into plant pots, then raised transplanted into a bigger pot, it's a bit more surgical but at transplant / sex the bottoms can be snipped off, it's more effort but I found the plants really loved the tallness.
I'd like to write more but it's 4am! I guess for those who like to experiment or have a reason they need to transplant then do so with care, for those who don't if you're having success start to finish in one size.. If it ain't broke don't try to fix it type of deal.
Cheers
Hello fellow growers I d like to share this with you, Pic 1 is my Amnesia Hase auto which I transplanted when it was 10 days from seed and the pic shows her on day 20 and pic 2 Amnesia haze not transplanted on day 20. Well from experience Ill never transplant my autos again. Funny isnt it same medium same light!!! of course I know that many do transplant with great result as they say and show yet Ill keep the safe side for now on:Grrr:
! She's almost now at 2ft and I'd say she wasn't stunted in the least bit, once the plant has a solid root mass holding the medium together I've found transplanting and tiering an excellent source to pop beans to get ready for perpetual gtows... While I got plants flowering taking up all my tent space I got a bunch of little seedlings awaiting the go ahead to be up planted.... 
