Skyscraper ad size
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160 × 600 for the wide skyscraper. The older 120 × 600 still exists but is largely superseded, and the 300 × 600 half page is the same height with twice the width.
How to use the skyscraper ad size
A skyscraper is a vertical strip in a sidebar, and 160 pixels of width is genuinely restrictive — a logo and a stacked line or two is the ceiling. The half page at 300 × 600 occupies the same slot on many layouts, gives nearly twice the area, and generally performs better for that reason, so it is worth checking whether the placement accepts it before committing to the narrow version. Both are desktop formats; sidebars mostly disappear on mobile layouts, which is why vertical display formats have declined in share.
Questions
160 × 600 for the wide version. The older 120 × 600 is largely superseded.