I own my home, no mortgage. Took 2 home equity loans out w/ my fiance, now ex, he left. I am co-signer. Can he take his name off? Can he take my home?

I am unclear by your post.  Is your fiance the lender, or a bank.  If a bank, you do have a mortgage -- the two lines.  No bank will remove a borrower name.  If your finace is a co-borrower he cannot take your home but the lender can if you do not pay.  Someone needs to look at your papers.