It’s important to remember that Ancient Greece was not so much a single entity as a collection of city-states that alternately fought with each other and got along. How great the power of the kyrios actually was depended largely on where she lived and her citizenship status. In general, a woman could not marry without permission of her kyrios. A woman could own property but without her kyrios she couldn’t make economic transactions over a certain value. It’s worth pointing out though, that as it was her property, he couldn’t do anything with it without her either. Not all of these necessarily held in all city-states, but these seem to be the common restrictions.
The two exceptions were Athens and Gortyn (on Crete). In Athens, all property within a family was part of the oikos and was therefore under the management of the kyrios. Legally, a woman could not make transactions greater than the value of a bushel of barley. According to Dio Chrysostom Athens was much more restrictive in this than other Greek cities. We do have evidence of woman accusing her kyrios** and having it appear in court. Even in Athens a woman’s kyrios did not have total power over her.
According to the Law Code of Gortyn, a woman’s kyrios still had control over who she married. He was still responsible for providing her dowry. Children born to a marriage still belonged to the father. He had, however, no power over her property. Anything she brought to her marriage was hers and her husband’s consent was not required for her to do anything with it. It’s important to remember, however, that these two cities, especially Gortyn, were exceptions rather than the rule.
*Minor children and elderly parents also had kyrioi. The latter case is not universal, but in Athens at least, a man could retire from public life when he got old and would then acquire a kyrios.
**In this case her father. It’s worth noting that she could not bring a case against him herself. Her family, however, could speak for her.
Schaps, David M. Economic Rights of Women in Ancient Greece. Edinburgh: University of Edinburgh Press, 1979.
Dio Chrysostom 74.9 (on the Athenian law) - Lacus Curtius
Lysias, Against Diogeiton 32.11-18 (the Widow of Diodotus) - Perseus
Excerpts from the Law Code of Gortyn - Diotima