TRUNKS & STUMPS
There are several ways to deal with the trunk (AKA bole) of a tree. The ways rarely get consideration and several of the options will challenge, especially depending on where you live and the type of landscape you like and can tolerate. I have employed all of the methods and can recommend each, but the circumstance, especially the location and the specimen, will dictate which of the options listed below is best or preferred.
(1) EXTRACT - The standard temptation is to make the thing quickly go away. If small enough, in the right location, and given the necessary tool/machine, the stump can be pulled or mechanically dug. But extraction is expensive, can cause massive habitat disturbance, and dealing with an extracted stump is an issue. Organic waste facilities typically will not take stumps. Moreover, the weight, which will inevitably include some substrate, can be daunting. Another extraction option is manual digging/chopping. Trust me, digging/chopping out a stump is perhaps the most difficult activity a gardener might ever attempt -- taxing and dangerous. SIDE NOTES: as a teenager I was employed to manually remove and gather uprooted stump remnants from a wooded floodplain along the Little Wabash River in south central Illinois. The area was being cleared for agriculture -- ill-advised land use given how often the area inundated. The work was done after the forest was destroyed -- the logs removed, the stumps bulldozed, and the slash burned. My brother Jim and I would follow a slowly driven tractor pulling a flatbed wagon on which we would pile the remnants. Those pieces too big or still partially buried were attached to the wagon and pulled out and away. The pieces were relocated to burning piles. It was exciting pioneer work, but hard and perilous. I will forego discussion on the use of explosives. BTW, the wood in the primary center portion of the root near the base of the bole can have spectacular split-resistant graining -- fabulous for woodworking.
(2) GRIND - This is the go-to method for most urbanites. What they usually fail to realize is that the grinding typically goes no more than 6-8 inches below grade thus the grinding will generally leave a substantial woody portion which will take many years to decay. Length of time for the decay will depend on the location, condition of the wood, species, and age/size of the specimen. Moreover, the decay eventually will produce a depression. Most of the time it will be impossible to plant a replacement tree where the stump was because it partially still exists. One can plant anew above IF willing to (1) start small and (2) add enough soil to prevent having to dig -- I am talking 8-10 inches which with the necessary slope will require at least 1/2 ton. If doing this one should always beware of the increased dryness caused by the raise. See also BURY, below. Further, some species are quite tenacious, e.g,, a black locust stump, even after grinding, will resprout prolifically (from the perimeter of the stump as well as from the lateral roots) and it will continue to do so for several years).
(3) LOW STUMP - In certain circumstances I simply pull the soil back from the base of the tree and try to cut the stump flush with the ground. In doing so the chain of the saw will inevitably encounter some dirt or rock. This type of cutting will quickly dull the teeth thus most extractors are unwilling to cut as low as I describe. Be willing to pay more to have this done. NOTE: the basal sprouts produced from stumps (referred to as coppice growth) will NOT produce a good tree. The interface, the union between the sprout and the trunk, is weak and the new stems frequently can be easily snapped/broken off. Moreover, the leaves on this growth will be abnormally large.
(4) BURY (Bed Over) - When cut low I will sometime merely cover the stump with soil (at least 6-8 inches) to mask the stump, thus creating a tapered raised bed. Depending on species and condition, the decay may take a decade or more and, as noted above, the area where the wood is decomposing will subside, leaving a depression. The covering soil helps mitigate.
(5) BURN - In times past this method was attempted more often. Numerous large diameter holes (at least 1/2 inch) were drilled into the stump and filled with an accelerant (fuel oil, not gasoline) and allowed time to soak into the wood. This technique will not work with freshly cut live specimens. Moreover, the burning often merely chars the surface which retards the natural decay process. Burning stumps is also illegal in most communities. An old-time method using saltpeter is described in my Rantings book on p. 279.
(6) SPEEDING DECAY - Cut low, drill large holes, fill with nitrogen rich fertilizer, and keep the wood moist. BTW, yew stumps are among the most rot resistant and, in general, hardwoods take longer to decay than conifers.
(7) SUBSTRATE FOR CULTIVATING FUNGI - As mentioned above, fungi are the primary decay agent. Yet some fungi produce reproductive structures that are scrumptious. So, why not consider inoculating the stump with spores of edible fungi? This method will both speed decay and yield food. See Fungi Perfecti (Olympia WA) for inoculum source. The tree species will determine which fungi you can use and it is important to keep the stump moist.
(8) PRESERVED LOW STUMP - All stumps will eventually decay, some faster than others. To retard the decay, drill some smaller holes (say, 1/4 inch diameter) and fill them with a fungicide. Fungi are the primary decomposers. It also helps to keep the wood dry and to seal the cut surface, but only after the specimen is dead (i.e., no growth or sap transport).
(9) LOW PLATFORM STUMP - I frequently leave a low stump, say 1-4 feet tall, and use the level flat cut surface for a platform to sit on or as a table on which to place objects (e.g., a potted plant or inanimate decorative item). Low, level, and flat stumps also are commonly used as chopping blocks.
(10) HOLLOWED STUMP - If naturally hollow by decay (heart rot) or through removal with a chainsaw, one can create an interesting natural container for a pot or potting soil. I like to use some vining plants, and remember to water when necessary. You might consider lining with plastic. If the wood is solid and there is no opening to the outside, one should drill a perforating downward hole at the bottom of the excavated area for drainage. See #7 above for ways to slow decay. Related, I enjoy seeing plants epiphytically growing in decaying knot holes or crotches -- common in the tropics and high rainfall temperate locations, but not in the Midwest.
(11) TALL STUMP w/ PART OF LOG ON GROUND - A large log (bole when standing) can make an excellent, ever-changing, long-term planting option. Perfect for a more naturalistic look, and one wildlife will love, although most of your sheared shrub neighbors likely will hate it. I also recommend removing any woody saplings that appear along side -- do so before they establish. After a couple of years the bark will start to detach (i.e., the log will become decorticate). After a decade or so the log will start to disintegrate, gradually creating a wonderful raised bed, sometimes referred to as a nurse log. The bed will be about twice the diameter of the original trunk. Leaving the log also means you will not have to pay for the removal nor will you ever again need to mow that area. While I remove and dispose of the tops and side branches (the slash) I also occasionally leave large trunks (at least 2 ft DBH) which were either snapped or wind thrown (thus with tipped up roots). I do this more in less manicured areas. These methods may infuriate your neighbors, but it's your property and it's nature's way (remember Spirit?). I view the remnant as a marker for (a statue of) a formerly living chlorophyllous denizen. Dare I say friend?
(12) BOLED - I also frequently will leave a tall stump (10 to nearly 20 feet) as support for various clinging vining plants (my fav is Virginia creeper) and for wildlife habitat. See the pic above for how truly magnificent the look can be. Behold Nature's beauty! FYI, notice the PI {R side} which is another of my favs, and I would have removed the thinner top section of the trunk pictured. I sometimes will leave a part of interesting large lateral branches. I also occasionally add an artistic embellishment -- something quirky. It is important to have the bole short enough so that when it falls over or crumbles the remnant will not cause damage to structures or vehicles. It eventually will come down -- nothing lasts forever, Moreover, if the tree was living when cut, you may need to girdle the bole to prevent epicormic sprouting. Boling also reduces the cost of removal. Finally, while not a technique I employ, the bole can be used to create some sort of chainsawed totem sculpture. SIDE NOTE: rarely will saw mills, now almost an anachronism is most communities, be interested in trees near habitation, especially the lower 4-5 feet -- too great a chance for encountering nails or inosculated metal fencing that would dull the saw and are dangerous for the sawer.
Most of these methods are definitely not for the clean city and suburban folk. They prefer an approach (a look) that is sterile and artificial. If employing one of my suggestions your neighbors may give you grief, but what do they know? Besides, WE need to explore some different ways of living (more environmentally harmonious landscape management) if WE are to have any chance of a future. The meatball shrub, lollipop tree, and drug dependent rug approach is NOT sustainable. Moreover, I have come to abhor that look, as well as rejecting/avoiding those who promote and employ it. At 70 I am tired of having to be an environmental evangelist AND most people don't want to hear it because they don't care -- content in their blissful ignorance. Divorced from Nature with a ME and NOW "convenience at any cost" attitude. I am ever more willing to excoriate misquided action in hope of effecting change. Different can be better.