In order to understand the occurrence and development of inhomogeneous poly-Si texture in the polycrystallization process of poly-SiTFT fabrication, we have simulated 1) the influence of pulse energy (PE) and optical axis (OA) fluctuations on the texture of poly-Si films and 2) the interference between both fluctuations, under the single-pulsed XeCl laser irradiation at the overlapping ratio 98%. The frequency of fatal irregular pulses in the PE fluctuation is much more than that in the OA fluctuation (pointing stability). Once the poly-Si texture suffers a fatal irregular pulse over the complete melting (CM) point, the inhomogeneous texture caused is never recovered by the following overlapping irradiation and no columnar structure is formed. However, when no irregular pulses exceed the CM point, the partial inhomogeneous texture caused in the poly-Si films is recovered by the thinning out of small Si grains in the texture and a columnar structure is formed. The key to the issue of fatal irregular pulses should be not only the reduction of PE and OA fluctuations but also the optimum selection of pulse energy not over the CM point.