Yeah I was thinking mainly Mario and Pokemon, and maybe Zelda.

Everything else, not so much.

i dont think so. To much competition

No, I don't think that Nintendo games would fare well on Xbox or Sony platforms. For better or for worse, Nintendo doesn't follow industry trends. Nintendo at their best defines what's "cool" and sets the industry in a new direction. At their worst, Nintendo holds on to a niche group of highly dedicated fans who are OK with Nintendo being different. On XBox or Playstation, however, Nintendo would be forced to play by the rules of the rest of the industry. Nintendo would be "performing" for an audience that doesn't care for their cute little quirks, an audience who wants super realistic gameplay, industry-leading online support and game controllers that don't come with surprises. It would be like putting a clown out on stage to do magic tricks for fans who paid to see a WWE wrestling match. It's just the wrong audience.

No, if Nintendo went multi-plat they would follow the path of Sega very quickly. Nintendo needs it's own exclusive environment, they just need one that invites people to come in and join the party not one that builds up walls like the Wii U did.

Would sale considerably more, Kart would compete sales wise with COD and GTA. Other major ones would be in the 10/15m range. Niche would be pulling in Bloodborne type sales on PS4 it self. On the nostalgia factor alone they would succeed massively, does not hurt they make good games either. And that they would lack any direct competition from any other publisher.

And to those saying it wont happen, it already is. Nintendo games their ip's on hardware not Nintendo made is them going 3rd party. Just small early steps. So with out the so called magic or relationship of Nintendo hardware people will be playing Nintendo games on their ios and android devices.

I honestly don't think that the sales of their franchises would increase by much (or really at all). I mean look at just today's NPD, that's what is selling to your average consumer these days.

Plus in Japan (arguably their biggest market accounting for population size) people would buy less from them because then they would need to make investments in a console they probably don't want that much.

Another thing is that I can't help but feel that if they did go 3rd party the quality of their games would see a decrease. Think about it, you're going from having your own machine that you know from inside out, to using someone elses. Something's got to give at that point.

Their established titles would, but I doubt new IPs would..

And the smaller ips would probably sell less, or equal  but at greater cost. They would most likely be deemed bad investments, relegating nintendo to a mario, Zelda, and pokemon factory. 
People who think nintendo going third party is a good idea only have an interest in one or two major ips. 

I feel like the big names like Mario and Zelda would do better and maybe stuff that fits in well with the other console's demographics like metroid and xenoblade but I don't think the smaller IPs like Kirby, pikmin, toad, ect would see any real benefits. If anything going third party would end up hurting smaller IP because they would have to compete with so many other games

So what about a game like Splatoon? Say Nintendo came out with a game like Splatoon as a 3rd party? 

That's the thing, I don't think it would have done as well

Splatoon is a shooter, meaning it would be competing against established games such as CoD, Halo, etc. so it could possibly have done worse that as we see now.. Hypothetical of course, because it didn't happen so it could go both ways.. but you'll never know :/