We discuss two methods for the ex-situ furnace growth of pure TlBaCaCuO superconducting thin films on LaAlO3(100) substrates. The traditional approach of "crucible processing" is used to grow high-quality films of several of the TlBaCaCuO phases. "Two-zone processing" promises greater thermodynamic control, yet film properties from optimized films are not as good as those grown from crucibles. The transport kinetics of Tl-oxide vapor from a source to the film surface appears to be a dominant factor. The best results are from single-phase Tl-1212 and Tl-2212 thin films. T-c's are high and sharp, J(c)'s > 1 x 10(7) A/cm(2) at 5 K, and surface morphologies are relatively smooth.