Normally, a divorced couple either puts the home on the market and splits any proceeds, or if one of them is keeping the home, then the other must refinance into just their name, to both remove the other from the mortgage and deed.
Either one of those options takes as long as it takes. The first takes as long as it takes to find a buyer, and the second could take as little as a couple of months if the party is credit worthly, or might never happen if the party is not.
But he stated that they were waiting for the home deed to transfer, not the mortgage to be refinanced or the house to be sold, although saying that they're waiting for the deed to transfer before they both move out doesn't make sense unless they're selling it.
If they're simply transferring the deed, it shouldn't take very long - if you're in a hurry, it could be a matter of days in my state, but possibly a bit longer. It depends on your rules for title search and so on. If it has been several months and the deed isn't transferred, then something has probably gone wrong.
BTW, since OP didn't mention a mortgage refinancing, I hope he's not transferring the deed without getting the other person off the mortgage (either by refinancing or by agreement with the mortgage company). If he's representing the person who's giving the house up and you don't get them off the mortgage before signing a quit claim or transferring the deed, then he's not doing what's best for them.
