Cracking & Foundational Movement
There are many factors that can effect your homes foundations and one of the major causes are tree root systems. They generally grow towards areas where moisture is retained under floor slabs and footings.
Most movement experienced by homes relating to tree root systems generally occurs in extended dry periods where tree root systems reduce moisture content causing soil to shrink and contract when cracks will appear in your home.
The best option to prevent foundational movement and cracking in the first place is to remove trees growing close to your home particularly larger types likes Eucalypts, Ficus / Figs or other varieties with intrusive root systems. Additional foundational performance information can be found at http://www.residentialreports.com.au/wp-content/uploads/2015/03/Foundation-Maintenance.pdf
If the tree is on an adjoining neighbours property this may present problems with removal. You can still remove any branches or root systems growing in your property. Having the owner of the property remove trees that effect your home and compensate for damage is a matter where you should seek legal advice. Additional information can be found at http://www.legislation.qld.gov.au/LEGISLTN/CURRENT/N/NeighDisputesDFTA11.pdf
With any cracking it is best to seek expert advice from a building inspector and engineer and monitor it to ensure movement does not continue. Technology has improved to a point where remedial works can be carried out by specialists with non-intrusive methods.