This is a complex enough question that really a simulation with sweeping variables is the best way to answer your question. It kind of depends on your base Waveguide structure (how tightly confined, how close to being multi-mode, aspect ratio etc.)

Regarding the bend losses, if you WG is single mode, then in most regimes makes the WG narrower increases bend loss. However, often the losses increase only very little until you hit something of a "critical" bend radius, at which point loss increases dramatically. This depends, though, on the thickness of the guide as well - for example, a very thick WG (perhaps multimode) will see nearly no increase in Bend Loss as it gets narrow (until it's very narrow), while a relatively thin guide may almost immediately start to see bend loss. I'm picturing the aspect ratio here - how multi-mode is the guide in both the Vertical & Horizontal directions. 

I haven't simulated a y-branch in a long time, but I believe one of the main considerations is how the modes overlap for various sections of the splitter - eg. the widest part of the splitter compared to where the two guides branch off - I think you want to maximize the mode overlap between these two, while maintaining a gradual, adiabatic transition. (Correct me if I'm thinking about this incorrectly.)

in in thinking about multimodality, I'd intuitively think that higher order modes have a larger Numerical Aperture/acceptance/emission angle, so the wider & more like a MM WG the structure is, the lager angle the modes would be able to efficiently couple to (so your output WGs could be at a larger output angle, and maybe tighter bend radius too).

You could try simulating it in CAMFR, which has a pretty good (free) 2D waveguide solver. Perhaps others will have more up-to-date intuition or simulations on your question. 

Thank you John, your response is quite insightful. I target single mode waveguide for 1559 nm wavelength In the range of 8-10 um width fabricated on MgO:PPLN. Is CAMFR free? May be I can give it a try.

Yes, CAMFR is free, but is a bit outdated by now so it can be a bit tricky to get the old Python versions you need working in concert (you may have to compile the packages since they're open source).  Perhaps start with the Python base of Continuum Analytics' Anaconda, but make sure you choose the Python 2.7 version. 

I think it's made to work with the older Python 2.5, which is what can make it tricky to get running. But the mode solvers are really great. You do have to code though, as opposed to having a nice graphic interface.

I saw on another one of your questions that you have RSoft - that should also be able to tell you similar answers. 

http://camfr.sourceforge.net/

Thank you John for your great advise.