What is the furthest star that can be measured using parallax?

If you look at something from two positions it appears to shift by some angle depending an how far away it is and the length of your baseline. If you look from opposite sides of the Earth's orbit, that is the longest baseline we have, and accurate measurements can be made out to about 3200 light years. Beyond that we are guessing. Highly scientific guessing, but guessing all the same. That is why when you try to look up the biggest stars, the figures get very uncertain beyond 3200 light years.