Arquette officially filed for divorce from Cox earlier this week, citing "irreconcilable differences" as the reason for the split. He also lodged his own divorce papers, and has not named a lawyer in his filing.
Cox's divorce papers make no mention of a prenuptial agreement, with sources telling TMZ that the couple have no such arrangement.
If there is no prenuptial agreement, the couple must evenly divide what they earned during their 12 and a half-year marriage.
Cox is reportedly worth $75 million (£48.3 million) and Arquette is worth $18 million (£11 million).
Both Cox and Arquette are seeking joint custody of their 8-year-old daughter Coco.
The Cougar Town actress is also seeking to drop her married name Arquette.
Watch a clip from Cougar Town below: