I am looking for articles that address a single mother's rights in the
state of Ohio.  Specifically I am looking for articles that explain in
layman's terms the process for establishing paternity, and how to seek
child support.  This is for an adult (technically) woman (not a
minor). Thanks

Articles?  I can't help you there, but worked with a father's rights
group in the 80's as modern support laws were developed. I was the
first person in our city/county to get a copy  of the official child
support recovery employee's manual, thus have some knowledge beyond
the average citizen.

It is really simple. Due to Federal laws, this is almost uniform in
all states. Differences will be minor.  (They are possible, but
unlikely.)

After the birth, contact the CSRU (Child Support Recovery Unit or
localized name) in your area. It is a government office.  Talk to
them; they take  care of the rest, period.

If they can find the putative (their terminology) father, they send
him a letter telling him to report for DNA tests; if he passes (flunks
from his viewpoint)  they then tell him to  report with income
information for support determination hearing. If he balks, their
lawyers take action in court, and if he refuses to come, they do it
without him.

Support amounts are based on state guidelines as required by Federal
law, thus not much negotiation.

They then send a letter to his employer ordering the employer to take
out the stated amount of money from each check, and shoud the employer
refuse, the employer gets to pay it.

It is down to a science, so don't worry about it.

Don't volunteer to pay a private attorney unless you totally strike
out with CSRU, since a private attorney can do no more than they can.

That sucks.  The guy should have some choice in the matter.  If a
woman can choose to abort, a man should be able to shirk his
responsibility as well.

If men wish to shirk responsibility then they can use condoms. Why
should some men assume that women bear responsibility for
contraception?

If a woman does not want to get pregnant and she has taken no
precautions, than it is plain foolish for her not to ask her partners
to "put the cap on the pen".