I think he should somehow be written off the show and some kind of younger child replace him as an unknown son of charlie,
because in the beginning of the show it was cute the things he says, now that he's become a teenager and basically creepy, his desire for sex in the show doesn't really fit the show, charlie is supposed to be full on bachelor and make the creepy teenager who looks like he hasn't showered in years go to boarding school for something bad he did. and it's not 2 and a half men anymore, Jake is bigger then Charlie.
so in closing, write him out

My view this is as Jake has been growing up the show has had to change a bit, and I dunno if it was for the better or worse, but the show isn't what it used to be, if that is Jake's fault or if the show has just been on for too long I can't say.

I kinda like Jake's character, so I would like for them to keep him on, but right now the big question is will there even be a 8th season as news that Charlie Sheen doesn't want to do the show anymore has surfaced.

But the idea of Charlie having some kid somewhere and having him move in there could actually be great, thats a great idea