Our complex is surrounded by trees. They are large established trees both in common area and in private courtyards. The council insisted these trees remain when this complex was built. Therefore they existed before the complex. There are units that have their decks built around these huge gum trees.
We have had problems with overhanging branches, over the neighbouring courtyard and/or over the neighbouring roofs. The OC has taken care of removing these.
With the OC being responsible for any large overhanging branches, at least they are in control of protecting against damage to common property (eg the roof, fences, walls). Don’t know how easy it would be to get an owner to pay for a branch removal if it was needed.