To me an 'established' tree is one that has been in place for one year- through all my seasons.

"Especially as the previous owner had it replanted after a few years, and has been doing non-deep irrigation"

If it has been in the ground in the same spot for a year or more it is 'established.'

It did need deep watering after having been moved, but if that was more than a year ago (I am unclear what you mean there ^) it is established.

Watering trees "less" after they are established only means less frequently and not less deeply. Any time watering is called for it needs to be done deeply.

There is actually a horticultural definition for this term :-)

You can get away with a single growing season for most perennials and some shrubs to be considered established but trees typically take longer. How much longer is determined by the climate, the size of the tree and the planting conditions.

Technically, a tree is considered established "when many roots will have grown a distance equal to approximately 3 times the distance from the trunk to the branch tips" (Gilman 1988; Watson and Himelick 1982). During the establishment period, shoots and trunk grow slower than they did before transplanting. When their growth rates become more or less consistent from one year to the next, the tree is considered established. To this is added the caveat that in "climates that receive average rainfall, by the end of the establishment period a tree has regenerated enough roots to keep it alive without supplemental irrigation in a landscape where roots can expand uninhibited by urban structures. In the drier parts of central and western US, the turf and landscape irrigation system may have to supplement rainfall to provide enough water for survival after establishment. Trees in unirrigated landscapes in dry climates may need supplemental irrigation beyond the end of the establishment period. This is especially important if the trees are not adapted to the dry climates."

Bigger, older trees take longer to establish than younger, smaller ones. That's a given. But how much longer is variable. I find it best to follow this tried and true rule of thumb: allow one year or full growing season per inch of trunk caliper at planting. It's not deadly precise but it works and in most cases, is also fairly accurate.

i would say a tree is established ... when it is back to growing to expectation.. and has no need of any water from you ... and that is usually when it re-established its root mass as gal notes ... of course the problem being.. you cant see the roots ...

it is very common for a tree to have a reduced annual growth rate after chopping off most of its roots ... e.g. a tree that should grow lets say 3 feet per year.. is only growing a foot ... and then on observation ... the next year.. 2 feet.. and then.. in year 3.. its finally back to the expected norm ... one might assume it has established itself ...

all during that time.. you are responsible for all watering based on the weather variable ... though as the years roll by .. you should be weaning it ..

you might also observe.. that a fruit tree does not fruit... maybe flower.. but not form fruit .. or aborts the fruit ... because the vagaries of weather cant be offset by the truncated root mass ...

a non -established tree might also go dormant a bit early .. or have some winter damage ... again due to its inability to store enough moisture to get thru winter ... in this instance.. its more about conifers and evergreen shrubs ... you dont mention where you are.. so i dont know what winter means to you ...

proper watering would be infrequent DEEP watering.. into the effected root mass .. are not a surface level ... frequent surface watering.. or leaf wetting would be just about useless... its not where its growing roots ... and of course your soil type dictates how water gets down to root level ...

soooo.. that is how i would observe and determine a plant becoming established .... its not really any different with any transplanted plant ... but in regards trees.. its all about tree time.. which is counted in decades .. rather than a few weeks or months with say.. a perennial ...

welcome to the forums.. and include big city name in every post ...

ken