The Ginzburg-Landau functional and the resultant phase diagram of quasi-two-dimensional superconductors in strong fields perpendicular to the layers, where the Pauli paramagnetic depairing is not negligible, are examined in detail by assuming the weak coupling BCS model with a dx2−y2-like pairing. It is found that the temperature at which the mean field (MF) transition at Hc2 changes into a discontinuous one lies much above another temperature at which a line HFFLO(T) of transition to a helical vortex solid similar to a Fulde-Ferrell-Larkin-Ovchinnikov state may begin to appear. In addition to MF results, details of a real phase diagram near the Hc2(T) line are examined based on a theoretical argument and Monte Carlo simulations, and it is found that the MF discontinuous transition is changed due to the fluctuation into a crossover which is nearly discontinuous in systems with weak enough fluctuation. These results are consistent both with the MF discontinuous behavior and a suggestion of HFFLO(T) in the heavy fermion superconductor CeCoIn5 with weak fluctuation and with their absence in cuprate and organic superconductors with strong fluctuation. © 2003 The American Physical Society.