Numerical simulations of three-dimensional infinite Prandtl number thermal convection with Rayleigh number (Ra) up to 108 are reported. Convection with Ra higher than 107 is characterized by the appearance of disconnected thermal plumes. The smaller plumes are detached by the currents produced by the larger plumes. The low wavenumber portion of a thermal power spectrum near the boundary layer becomes flat at high Ra, while the spectrum measured in the interior shows a positive slope for low wavenumbers. Differences are found in the thermal spectra between 2D and 3D models. ¿ American Geophysical Union 1993