Possible to extend polygons to fill gaps in parcels?

[RachaelJohnson]

I searched and there's one question similar to mine, but it didn't have any responses. So, I'm trying again. 

I am using ArcGIS 10.3.

I have a parcel layer that doesn't include the roads. I need parcels bordering empty space to extend to fill in the gaps, sharing the area evenly with opposite parcels.  I provided an example of what I need to accomplish.  I did the work in the example by hand, but I have a whole city to do.  Is there a built-in tool that does something similar?  Or a series of steps that can approximate the desired result?  

Thanks for your time. 

[ChelseaRozek]

Did you find a solution for this?

[KBKnight]

yes, inquiring minds want to know!