The alignment of polyatomic molecules under strong 35 ps laser irradiation is investigated for a broad range of laser intensities (10(13)-10(15) W/cm(2)) using time-of-flight mass spectrometry. The dynamic alignment of the molecules under study (C2H5X, X = I, Br, Cl) is verified in single-pulse experiments by recording the fragments' angular distributions, their dependence on the laser intensity, and also the comparison of the ionic signal of the various fragments recorded for linear and circular polarization. For all cases, the angular distributions of the Coulomb explosion fragments are found to be independent of the laser peak intensity, implying that the molecular alignment is taking place during the rise time of the laser pulses at relatively low intensities (1011 W/cm(2)). Moreover, the same result implies that the alignment mechanism is close to the adiabatic limit, albeit the laser pulse duration is much shorter than the characteristic rotational times (1/2B) of the molecules under study. Finally, by comparing the angular distributions of the different molecules, we conclude that the degree of alignment is only weakly dependent on the molecular mass and the moment of inertia under the irradiation conditions applied.