Hello!
Recently I came across articles about the Design Challenge competition from Mozzilla Labs. Looked presented videos with variants of tobacco substitutes. Some liked, some not. Although the contest has already come to an end, but I also decided to submit to the Habra viewers a choice of replacing the tabs.
The main essence of the idea, of course, is to make a clear and convenient tool for managing open sites.
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For the basis of my concept, I took a ready-made development called “Express Panel” (as it is called in Opera). The point is to group several pages of the same domain (for example, several open Google pages).
It looks something like this (this is a prototype and I don’t pretend to be a designer):

Naturally, the cells should be displayed as many as open sites (in the figure I just showed how it will look in the total mass of open sites). The cell in which the site is located and which has several pages open is highlighted in a different color and in it, for example, the number of open pages for this domain is displayed in the corner.
After the user hovers the mouse cursor over such a cell, a block containing the cells of the open pages associated with the domain will open. Example in the picture:

If there are more open pages for the domain than, for example, 12 pieces, then in this case the thumbnails will be converted into a list with page headers.
In a group, you can close both individual pages and the entire group (there are crosses in each cell). By the way, the location of the crosses is not accidental. This is done so that the user does not accidentally close the entire group.
How to call the panel itself? Well, there may be several options, but the most convenient, I think, is to make a way for the user to move the cursor to the left edge of the browser window, after which either the panel opens immediately or a shortcut appears that you need to click to open the panel. Approximately how one of the taskbar display modes is arranged - when the panel is not needed, it crawls down, when needed, we move the cursor and it appears.