We have investigated the angular distribution of photofragments resulting from multiphoton above threshold dissociation (ATD) of HD+ from initial bound levels nu(i) = 0, 1, 2 and J(i) = 0 induced by linearly (up down arrow) and circularly (curved right arrow) polarized laser fields of intensities I= 1. 5, and 10 TW/cm(2) and frequency omega = 30 333 cm(-1) (lambda = 329.7 nm). The time-independent close coupling (CC) method has been used. Molecular rotation has been taken into account by including 72 channels with J = 0 - 7 and number of photons n = - 1 - 7. for up down arrow polarization. In case of curved right arrow polarization, the channel number reduced to 48. All the radiative couplings including those due to the intrinsic dipole moents of HD+ have been considered in a truncated length gauge form of interaction. For (net) one-photon dissociation (front nu(i) = 1, 2) by bond softening, the alignment of the angular distribution of photofragments increases with intensity (1-10 TW/cm(2)), for both up down arrow and curved right arrow polarizations. The angular distributions for (net) two-photon fragmentation via the adiabatic paths are sharper, for both up down arrow and curved right arrow polarizations, than those for (net) three-photon dissociation by nonadiabatic transition. With increase of laser intensity, the alignments in the angular distribution of the two- and three-photon peaks (from nu(i) = 0) change differently for up down arrow and curved right arrow polarizations. In general, at a given intensity, the photofragment angular distributions about the space fixed Z-axis are different for up down arrow and curved right arrow polarizations. The Z-axis is along the direction of polarization vector for up down arrow polarization, but along the propagation vector for curved right arrow polarization. The degree of alignment in the angular distribution of the photofragments for up down arrow polarization at a lower intensity is expected to be the same as that at a higher intensity for curved right arrow polarization. We have endeavored to interpret our results of the sharpness of the photofragment angular distributions of HD+ as functions of intensity for different open photon channels within the framework of the dressed state picture and the bond softening, adiabatic path, and nonadiabatic transition mechanisms. We have also computed the branching ratios of the photofragments of HD+ to different open photon channels for both up down arrow and curved right arrow polarizations of the laser fields.