Molybdenum is a low Tc, type I superconductor whose fundamental properties are poorly known. Its importance as an essential constituent of new high performance radiation detectors, the so-called transition edge sensors (TESs) calls for better characterization of this superconductor, especially in thin film form. Here we report on a study of the basic superconducting features of Mo thin films as a function of their thickness. The resistivity is found to rise and the critical temperature decreases on decreasing film thickness, as expected. More relevant, the critical fields along and perpendicular to the film plane are markedly different, thickness dependent and much larger than the thermodynamic critical field of Mo bulk. These results are consistent with a picture of type II 2D superconducting films, and allow estimates of the fundamental superconducting lengths of Mo. The role of morphology in determining the 2D and type II character of the otherwise type I molybdenum is discussed. The possible consequences of this behaviour on the performance of radiation detectors are also addressed