Thanks Dimitar for your quick answer - yes, you're right, the caret coordinates are changing when the cursor is moved/clicked in different portions of the text.
In fact, what I'm trying to do is to write in a multipleLine textbox few lines of text, each of them ending with a LinkLabel, which once clicked, will open an excel file for editing (or whatever....). Running the small piece of code, the LinkLabels are not visible, nor active in the tetxtbox (moving the mouse over the textbox, seems that all Labels are put in the upper left corner of the textbox - at point (0,0), one each over the precedent one. See attached 2 captures: one representing the form with the textbox but without a proper hyperlink (no hand cursor, no clickable text, no underline....), the second the very small piece of code.
Any suggestion about this approach will be really appreciated! (probably, the best solution would be to implement a new Control - a proper HyperlinkLabel, or to use a RichTextcontrol, but for the moment, I would like to know if it's possible to use this way, using a TextBox.