Universal adversarial perturbation (UAP), i.e. a single perturbation to fool the network for most images, is widely recognized as a more practical attack because the UAP can be generated beforehand and applied directly during the attack stage. One intriguing phenomenon regarding untargeted UAP is that most images are misclassified to a dominant label. This phenomenon has been reported in previous works while lacking a justified explanation, for which our work attempts to provide an alternative explanation. For a more practical universal attack, our investigation of untargeted UAP focuses on alleviating the dependence on the original training samples, from removing the need for sample labels to limiting the sample size. Towards strictly data-free untargeted UAP, our work proposes to exploit artificial Jigsaw images as the training samples, demonstrating competitive performance. We further investigate the possibility of exploiting the UAP for a data-free black-box attack which is arguably the most practical yet challenging threat model. We demonstrate that there exists optimization-free repetitive patterns which can successfully attack deep models.