As a former Delphi developer, I sympathize. It used to be that you could find a free component with source for just about anything. You probably know about the Delphi Super Page (my old go-to source for everything Delphi). I looked; no mind-mapping components, there. (Of course, the site has not been updated in about 2 years).
I do have a suggestion, though, but it's not optimal: StarUML was written in Delphi, and it contains custom components for creating UML diagrams. The source is available for download, and it seems to me that the UML primitives (boxes, lines, clouds and such) could be adapted to your purpose. The web site is http://staruml.sourceforge.net/en/.
I know it's not ideal, but at least you would not have to start from scratch.
Good luck!