For the Z3's I've always used what we generally refer to as 'red tape'. It's a strong-bonding clear double stick adhesive. There WILL BE LIGHT LEAKING FROM THE EDGES. It's simply because the original adhesive (glue) pulls the screen down more tightly and it's opaque. The clear adhesive isn't, but it holds very well. The same thing is common with the LG G series phones. I get all of my red tape from Etechparts.com. Use a little heat after (I use 65C for 15 mins on my heat plate) to help the adhesive bond to all of the surfaces correctly and clamp it tight while the adhesive cools.
For the Galaxy S5's and especially the Note 4's (which are notorious for coming loose) you have to get high quality adhesive. The stuff on Ebay won't cut it. I've gone to Etradesupply.com for all of my Samsung adhesive needs. I've even tested their S5 adhesives with the water test. They retain the water resistance as long as the frame isn't tweaked. Again, 65C for 15 mins on the hot plate after, clamp and let cool.
I've noticed the largest difference between a screen staying or lifting on me a few days later is the heat. When the adhesive heats, it gets pressed outward, applying to the whole surface. Then clamps for cooling! If you don't, the heat will just loosen it. If you clamp it, it spreads the adhesive out further, and the cooling contracts it, sucking the screen down to the frame. Great method for iPads too!