First, vertical cuts do not make the trunk thicken; they just produce vertical scars. Sometimes the lip of the scar protrudes slightly and self proclaimed 'gurus' claim the bole is thicker. People have also advocated punching the trunk with knife tips, but 'going Psycho' on it is just a way to make your tree vulnerable to a serious fungal infection. It has also been advocated that one literally hammer their trunks - the problem is that it is almost impossible to avoid killing the cambium in some places (so, at best, it produces mixed results).
A trunk/branch thickens more rapidly the more foliage it carries. It also thickens faster if the extension growth is allowed to run. Decapitating a branch will slow the rate of its thickening, but with many species the increased leaf area that comes as a result of ramification can more than compensate for the setback. This process, though, produces a stem with negligible taper. Therefore, one eventually must prune off most of it and start the process anew with another ‘sacrifice’ in order to make a tapered trunk.
With conifers great care must be taken to keep small lower branches alive – once they are gone, they are gone (ala Yogi Berra) because there is little chance of regenerating them. So the sacrifice is usually bent so that it will not shade those low branches. Likewise, foliage on the lower portions of the ‘sacrifice’ is also usually removed.
It is easier to control the growth in containers, but trunk thicknesses are practically limited 2 to maybe 3 inches. Thicker trunks need to be ‘field grown’ in mother earth. However, progress will be even slower for the first two or three years in the ground as the tree gets ‘established’. Once established, the sacrifice whip’s wagging in the wind will cause the base to thicken or flare. A negative, though is that the roots become a few heavy/thick ones with the fine ‘feeder roots’ far away from the trunk. It then is a challenge to subsequently generate fine fibrous roots close to the trunk and a nice nebari. This is avoided by container growing; in fact, growing in oversized containers of a bonsai substrate is just about the only means of developing the roots necessary for bonsai containers.
Applying a wire tourniquet to a trunk will eventually barricade the flow of sugars from photosynthesis and polar auxin transport (PAT) which results in a region of enhanced radial growth just above the tourniquet (i.e., a ‘flare’). If this is covered with a damp material such as sphagnum moss, vermiculite, pearlite, or a bonsai substrate, roots will eventually be produced (this is a trick to make an air-layer explant that has a nicely flared base).
Wire spiral wrapped around the trunk will have a similar effect as the wire ‘bites in’ over the course of a season or two. The wire can be left in place and eventually the growth will cover the wire though the traces remain visible for a number of years. An irregular/artistic wrapping pattern is needed to obscure this, but with junipers spiraling shari is much admired – this is a way to achieve it while hastening the thickening of the trunk.
With deciduous trees, one doesn’t need to worry about low branches as they can/will be regenerated with heavy pruning if not by spring budding. Hence, a branchless deciduous species seedling can be threaded though the hole in a CD, a hole drilled in a tile, a drain hole of an old ceramic pot bottom, or etc. and grown. As the tree thickens, will automatically generate a nice basal flare and ground layer itself (note: the ‘tourniquet’ is under the substrate surface). Analogously, one can start with an air layer and screw it to a tile/board – this will develop basal flare and eventually a ‘pancake’ nebari.
The last point about thickening is heavy applications of fertilizer will help. Lots of nitrogen, though, tends to produce long internodes, which we want to avoid in our bonsai (because branches and ‘back budding’ generally can only occur at nodes). So one wants to start with a seedling/sapling/trunk that has short internodes, particularly the last internode to be retained; after that one doesn’t care because it will be cut off. Then one wants the next segment to be suitably short – it will help to restrict nitrogen while it is being grown, then again switch to high nitrogen after it is set to thicken. Basically this nutritional manipulation is only possible in containers.