I wanted to verify you were actually talking about Cladophora aegagropila. When I grew these, I mangaged to turn my one ball into 5, in about a 8 month period. Over time you might be able to fill the bottom of a tanks with these guys.
If they are hit with an Ammonia spike, they will produce spores with will cause a bunch of these to form all over your driftwood and such.
I have not tried "spreading them out" as a forground. I suspect you could use a steel mesh technique such as is used to create a "Riccia Carpet".