Yes, I am predicting that no console (except Playstation home consoles) will outsell the Playstation Portable anymore.  

8. Generation?
Wii U & PS Vita are failures compared to PSP. They won't achieve this, even 20M lifetime should be a hard number for each one. 
Nintendo 3DS and Xbox One are not strong enough, they might get close but none of them are able to reach PSP lifetime numbers.

9. generation? 
Next Nintendo hardware: I think Nintendo won't bring us a surprise hit like the Wii anymore, the next Nintendo console will sell typical Nintendo numbers (20M-50M) and won't be a danger for the PSP. This also applies to the next Nintendo handheld, the handheld market is shrinking outside of Japan. Smartphones are getting more important in our society and there is no way to change this anymore.
Next Xbox hardware: The next Xbox could be an adversary for the PSP, but I think the next generation will again be Playstation dominated so 80M seems not likely for the next Xbox. 
New Playstation handheld: There will be no new Playstation handheld.
Google / Amazon / Samsung hardware: I don't expect them to have big chances in the video game market. They don't have the same experience like Sony, Microsoft and Nintendo.

Déjà vu.

This gen, you are probably right (depending on what Nintendo wants to do with the n3ds), next gen, too early to tell cause anything can happen

Why the PSP?

Next gen and the one after that are impossible to tell, I still don't know why you're going with the PSP numbers despite it's few successors flopping, Nintendo could say the same about Wii numbers but really they are just numbers and the console is now in the past and isn't supported anymore, just like the PSP is.

The thread is giving me deja vu where no one but Sony can do a ball park hitter, the Vita is just a minor tiny little speck of a setback while the competition apparently has no chance against all odds and mobiles are coming to claim all 7 billion of us and that there will be no market, so what if the handheld market is shrinking, at least Nintendo is still in the game and supporting it, it's not like mobiles are suddenly going to kill off all the hardcore handheld gamers, there's always going to be a market for someone, not take mobile or quit handheld gaming forever like some people are making it out to be.

If i can, maybe you have agree to say that THIS GENERATION nothing will outsell PSP withouth PS4 (but even nope, because 3DS have good possible for break 80m, even if i don't think), but for the NEXT GEN you can't know how will happen.

Just for exemple: Sony will failed, MS will sell the XBOX division, N will become the only production of game's, the third party will make the game on next Wii, and it will sell 150-200 million... just for exemple.

I want to show everyone what a beast the PSP is.
PSP = Best handheld ever

PSP had more support then psv+3ds combined.
If a handheld release with a much better support then PSP i'm sure this handheld will outsell it

I can easily agree on the PSV part but PSV + 3DS...  I can't believe that.  From what I remember most people just used their PSP (in USA) as emulators for NES, SNES, etc games.