The leaves with their slightly wonky base makes you think of elms. And indeed the European Nettle Tree used to be part of the elm family. As flagged by this common name, the ragged edges and leaf shape hint at the nettle.
While it has never been classified in the nettle (Urtica) family, Urticaceae, the European Nettle Tree is now included in a family whose closest relatives are the elms (Ulmaceae), nettles (Urticaceae) and figs (Moraceae). Celtis australis, as it's called botanically, joins Humulus lupulus, the hop plant (think beer, and sedative pillows), and Cannabis sativa, marijuana (think dope, and pain relief), and others, in the family Cannabaceae.
Celtis australis is sometimes called the Asian Hackberry, and in the two common names you have pretty much all of its native distribution - Europe through to western Asia. It was named botanically by Swedish botanist Carl Linnaeus so the epithet 'australis' would refer to south of Scandinavia. (The common name hackberry is in fact a corruption of hagberry, the name given to a bitter cherry growing up Carl's end of the continent)
Even in its natural habitat this is a group of plants that are frequently overlooked. A nature column in Colorado newspaper headed up its 2012 story on two local species with the line 'few trees hide so well in plain sight as does the hackberry'. It goes on to say the hackberry 'forms no groves as does the quaking aspen .. no savannahs as does the eastern cottonwood ... [and] no forests as do the oaks ...'
It seems the hackberries are scattered among other trees, and easily 'lost in the camaraderie of crack willows and boxelders'. In my local park - and in the Melbourne Gardens for that matter - the hackberry is lost among other more showy plants (e.g., in the park, a Cape Chestnut with it's brilliant pink sprays of flowers in early summer).
Our North American naturalist goes on to lament that the wood is no good for polo or croquet balls,golf club heads, tool handles, baseball bats, wine barrels, whisky casks or fine furniture... The most productive use that we humans have found for hackberry wood seems to be for crates and pallets. The trunks rather plain but often characteristically warty.
Although there is no record of hackberry being used for recreational pleasure or medicinal treatment, the fruits are edible. That includes the thin red skin (when mature - my pictures were taken in late January) as well as the relatively large, hard stone, which would have to be mechanically crushed first I think. Apparently the seed is 'rich in protein and fats'
In Victoria, two Hackberry species are already relatively minor weeds: our European Nettle Tree is described in VicFlora as 'weakly naturalised near Myrtleford', with a few records also near Melbourne, and the North American Hackberry is 'weakly naturalised on Yarra River flats near Heidelberg'.
Given it is rather weakly planted down this way, perhaps it won't be such a problem.