As far as I know, what Tesla claimed to be able to do, based on his Colorado Springs, was transmit power wirelessly. His Wardenclyffe project, on Long Island, was an attempt to implement this and also create a worldwide communications network. The wierless power transmission was apparently a mistake, and would have been problematic had it worked, as it would have been difficult to impossible to ensure that consumers of power paid producers.
After Tesla ran out of funding for Wardenclyffe, he pretty much became a crackpot. He made wild claims for "inventions" that existed only on paper or in his head, and the newspapers loved to interview him, but he produced very vew useful inventions in this time period (the Tesla turbine being perhaps the major exception to this). Unfortunately, the "free energy" and "over-unity" crowd worships the crackpot, and misinterpret his "wireless transmission of energy" claims as "free energy" claims. The Tesla who deserves to be worshiped (if anybody does) is the young Tesla who invented the polyphase AC electrical power system that we are still using more than a century after he invented it, not the pathetic crackpot he became later in life.