On the Galaxy Tabs, that black almost cloth-like layer of adhesive is very strong stuff. I've found that if I heat the glass a bit first to loosen the adhesive, I can actually remove the broken screen by getting between the adhesive and the glass instead of between the adhesive and the frame. That way, the original adhesive stays on the frame and can be reused to install the new screen. Reusing the original adhesive in this way holds the new screen better than any replacement adhesive I've found.
However, if that's not possible, I've found that the best double-sided tape for the job is 3M 300SLE. It's not the cheapest stuff but it does the job well. You can can buy it in rolls of different thicknesses on line. My advice is that after you install the new screen, apply heat around the edges to heat up the adhesive underneath a bit, then immediately apply pressure around the outside for about 45 minutes. I like to use small plastic clamps for this.
Also, whenever applying heat as mentioned above, remember that you don't want too much or you could damage the LCD underneath the digitizer or other components. 190 degrees is about the max most Samsung components can handle without being damaged.
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