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Recent statistics suggest that online social network (OSN) users regularly share video contents from video sharing sites (VSSes), and a significant amount of views of VSSes are indeed from OSN users nowadays. By crawling and comparing the statistics of same videos shared in both RenRen (the largest Facebook-like OSN in China) and Youku (the largest Youtube-like VSS in China), we find that the huge and distinguished video requests from OSNs have substantially changed the workload of VSSes. In particular, OSNs amplify the skewness of video popularity so largely that about 0.31% most popular videos account for 80% of total views. Another interesting phenomenon is that many popular videos in VSSes may not receive many requests in OSNs. To further understand these findings, we track the propagation process of videos shared in RenRen since their introduction to this OSN, and analyze the effect of potential parameters to such process, including the number of initiators (users who bring the video to the OSN directly from a VSS), branching factor (the number of users who watch the friend's shared video), and share rate (the probability that the viewers of a video will further share this video). Beyond our expectation, none of these factors determine a video's popularity in an OSN. Instead, it shows great randomness for the number of a video's potential requests when it is shared to an OSN. By modifying the basic Galton-Watson stochastic branching process, we develop a simple yet effective model to simulate the video propagation process in an OSN. Simulation results show that it can well capture the randomness of a video's popularity and the skewed video popularity distribution.