No it does not. The payment of taxes doesn't void titles to property. If at some point you wanted to force the issue of selling this property (or via a settlement of that case, forcing a buy-out of the other two), in a partition case, the court will usually start with an equal split of the sale proceeds but then make adjustments based on relative financial contributions. There's were your payments may come into play. However, if you are the one occupying the property, your payments might be just viewed as rent, duly owed to the three of you, and thus result in no adjustment in an equal split.
To questioners from West Virginia & New York: Although I am licensed to practice in your state, I practice on a day-to-day basis in Massachusetts. I answer questions in your state in areas of the law in which I practice, and in which I feel comfortable trying to offer you assistance based on my knowledge of specific statutes in your state and/or general principles applicable in all states. It is always best, however, to work with attorneys and court personnel in your own area to deal with specific problems and factual situations.