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Without a doubt the most important contributing factor to the experience you can expect when making use of the HDMI connection on a laptop to connect to an HDTV is the video card. There are many types of video cards that can be used by laptops, and
they are not all built the same.
Unfortunately, the existence of an HDMI connection doesn't always mean a laptop has enough power to put it to good use. The main offenders are some higher-end Intel integrated graphics solutions which support HDMI but sometimes struggle with 1080p resolution. They should be capable of 720p, however. Intel integrated graphics are also poor when it comes to 3D graphics.
Even the basic mobile GPUs offered by ATI and Nvidia are much better than what Intel makes available, and should be able to display 1080p video even on a system which is otherwise lacking in performance. Mobile GPUs can also provide much better 3D graphics performance, but they'll still struggle at 1080p resolution when playing a 3D game, with the exception of the very fastest models like the Radeon 4870M and the GTX 280M.