If my credit card company stopped some authorized charges, am I liable to the company that tried to process them?

You are not liable to the company for charges you did not authorize and for items you did not order.  Your boyfriend is liable for those charges, not you.  There are a couple of things that you can do to help improve your situation, though.  I'm assuming that you have advised them that you did not place or authorize the charges... if you haven't, do so and give them as much info as you have about your boyfriend.  Second, file charges against your boyfriend for using your cards fraudulently-- then refer the  phone sex company to the law enforcement agency working on your case.  They can seek restitution through that agency and court system for their losses as victims.  (Many collection agencies employ bullies-- and will usually back off once a law enforcement agency is involved.)  A third option is to get as much information from the people that you talk to about the phone sex company:  name of the person you are talking to, name of that person's employer, address and phone number for the company.  From there, send a letter advising them that you dispute the charges (because you did not incur the charges) and request that they cease collection activities against you.  If after this series of events they are still threatening you, consider two other options.  First, file a complaint with the attorney general of the State of Texas outlining your complaint.  The AG has an online consumer complaint form that you can use.  Second, you may want to contact an attorney to send a reinforcing demand letter.  Most bad collectors will cease after a demand letter from an attorney, but if this is an extreme company, you may also need the attorney to file a suit against the phone sex company if the harassment continues.  Regardless of which level you reach in these options, make sure that you check your credit report on a regular basis for the next few months to make sure that they haven't shifted to a different for of harassment by wrecking your credit history with a negative report.

If your credit card company stopped some unauthorized charges on your credit card where your former boyfriend used it without your permission, you are not responsible for paying any of the charges be it to your credit card company or the vendor that processed your credit card without your permission.

If the company that the charges were made to is pestering you, you need to write the company advising that your credit card was used improperly and that the contact that it is having with you could be considered an unfair and illegal debt collecion practice.

Keep a copy of the letter for future need.

Good luck.