URLMap.exe is part of Money 2002 and 2003 which runs alongside the program to provide additional functionality in Internet Explorer. It is known as MoneySide or Money Viewer.
The program isn't that essential to run when you're using Microsoft Money, and if your version of Money is later than 2003, then shouldn't be seen at all. If you want to disable this program, then you can do without affecting the core part of Microsoft Money. You can disable it by starting MoneySide (Money Viewer) and choosing the Help->Settings option. In there, there is a choice to 'Never Open MoneySide' (see
Keywords: Money Viewer, URLMap, MoneySide