I strongly believe this business is completely legal.
Providing research assistance is legal. What you are advertising is blatantly ILLEGAL.

It is a crime to knowingly enable students to engage in academic fraud by submitting your writing-as their own work-for academic credit. You may not:
* suggest, in any way, that a customer may directly submit a paper for academic credit;
* guarantee a particular grade;
* offer to write in a manner/style that will "fool" a teacher/professor;
* state that a student's teacher/professor will not "find out";
* suggest that your service is a "shortcut" for a student's academic requirements (or to graduation);
* offer "ghostwriting" (ghostwriting is expressly banned and illegal for academic works);
* offer to transfer copyright to the customer (you may legally sell your time/labor/research/expertise, NOT a physical/virtual, written work that would obviously require copyright ownership in order to turn in for academic credit; fraudulent companies offer copyright ownership for that precise reason);
* offer to take exams for a student;
* ask for a customer's school/course information;
* place "blank lines" at the top of a document so that the student may fill-in his or her name, professor's name, course, and/or academic institution.
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Here are some of the laws:
Californialaw.justia.com/codes/california/2007/edc/66400-66406.7.html
law.justia.com/codes/california/2005/edc/66400-66406.html
codes.lp.findlaw.com/cacode/EDC/3/d5/40/6/s66400
Connecticutlaw.justia.com/codes/connecticut/2005/title53/sec53-392b.html
law.justia.com/codes/connecticut/2011/title53/chap949b/Sec53-392b.html
law.justia.com/codes/connecticut/2011/title53/chap949b/Sec53-392a.html
legaltips.org/connecticut/Chap949b.aspx#Sec53-392b.aspx
Floridalaw.justia.com/codes/florida/2011/titlexlvi/chapter877/section877.17/
law.onecle.com/florida/crimes/877.17.html
Illinoislaw.justia.com/codes/illinois/2005/chapter18/1052.html
law.justia.com/codes/illinois/2012/chapter-110/act-110-ilcs-5/
Oregonlaw.justia.com/codes/oregon/2009/165.html
Mainelaw.justia.com/codes/maine/2005/title17-ach0sec0/title17-asec705.html
mainelegislature.org/legis/statutes/17-a/title17-Asec705.html
Marylandlaw.justia.com/codes/maryland/2005/ged/26-201.html
Massachusettslaw.justia.com/codes/illinois/2005/chapter18/1052.html
malegislature.gov/Laws/GeneralLaws/PartIV/TitleI/Chapter271/Section50
law.onecle.com/massachusetts/271/50.html
Nevadalaw.justia.com/codes/nevada/2010/title15/chapter207/nrs207-320.html
law.onecle.com/nevada/crimes/207.320.html
leg.state.nv.us/NRS/NRS-207.html#NRS207Sec320
New Jerseylaw.justia.com/codes/new-jersey/2009/title-18a/section-18a-2/18a-2-3/
law.onecle.com/new-jersey/18a-education/2-3.html
New Yorklaw.onecle.com/new-york/education/EDN0213-B_213-B.html
North Carolinalaw.justia.com/codes/north-carolina/2010/chapter14/article20/section14-1182
law.justia.com/codes/north-carolina/2005/chapter_14/gs_14-118.2.html
Pennsylvanialaw.justia.com/codes/pennsylvania/2010/title-18/chapter-73/7324/
Texaslaw.onecle.com/texas/penal/32.50.00.html
law.justia.com/codes/texas/2005/pe/007.00.000032.00.html
law.justia.com/codes/texas/2009/penal-code/title-7-offenses-against-property/chapter-32-fraud/
Virginialaw.justia.com/codes/virginia/2006/toc1802000/18.2-505.html
Washingtonlaw.justia.com/codes/washington/2005/title28b/28b.10.580.html
law.justia.com/codes/washington/2005/title28b/28b.10.584.html