IRS custodial/non custodial parent rules count the NIGHTS they are with you ... if they do stay overnight 12 weeks of the year ( 12 x 7 = 84 nights) then you are the non custodial parent according to the IRS and you cannot claim them without a signed 8332 from the custodial parent AND the boyfriend cannot claim them at all.
NOW if the child only visits you and returns home at night that changes the picture. Read the other comments and answers above.
