We have remodeled our house using the rounded corners....now we are ready to put the baseboard back in. How do you do the outside corners so that you don't have the gap at the corner ?

 

"rounded corners"

do you mean bullnose corner bead on the drywall?

 

It depends on the style of baseboard you are using, but it usually works well to just cut yourself a corner block out of your baseboard. The top of the baseboard will be (about) 7/8" long, with 22.5 degree miters on the left and right sides. Your baseboard will meet up to these miters on each side with their own 22.5 degree miters. You will have to play around with the length of that corner piece but that's the general idea.

There will be very small gaps on top, which will need to be caulked, primed and painted.