Part of my quest to learn how to ink paint was figuring out if the sponges I was using (some face make-up sponges I had lying around and sponges that came as filler with a set of hot-fix rhinestones) were appropriate for this type of project.
The black filler sponges came square and I tried rounding them so they wouldn't leave streak marks. After trying - unsuccessfully - to reproduce the ink painting I've seen on other sites I decided to buy actual ink daubers (craft sponges designed for this purpose). I wanted to see if the daubers were special in some way. The sponge on the daubers is a cross between the two sponges I was already using. It's got small pores and is quite soft to the touch as well as having a rounded top.
With regards to ink painting however, I had the same problems - streaking and hard edges. Obviously my problem was not the sponges then (or not just the sponges). So I tried something else. I tried not putting as much ink on the sponges. Voila! Apparently I was over inking the sponges, making their first contact with paper too ink heavy, so they smeared and left firm lines.
In addition to the over inking, I suspect you're also supposed to leave that first smear on whatever mask you're using with your project (for land/sun/landscape background), then smear a smaller amount from there onto your project. I'll have to practice with these ideas, but my first attempt with this knowledge turned out quite good. I'll post that card tomorrow. :)