Parallax is rarely, if no longer used to measure great distances in space. Astronomers have been using Cepheid variables and Type 1A supernovae for decades as they can be accurately measured to an approximate distance of over 20 million light years, versus stellar parallax measurements which are only accurate to about 300 light years, given that you're measuring angles in milliarcseconds. For even greater distances, astronomers rely on spectral red shifting.