Thank you for your advise, Chris! Just look the Wiki page as one (I was too much thinking in frames, actually). Some searching to the right class of the elements (is there an explaining list?) and it worked.
I even managed to get the search bar properly. I understand now the confusion: it's just a question of positioning: placing it on the part of the page you want with the absolute attribute.
But one thing I can't get wright: the toolbox (the element below the search). If you make portlet invisible, the bar above the pages disappear, even the tabs. I tried to change -in monobook.php- the div of class="portlet" in "ownportlet", and made that hidden (line 177 and even, when that did not work, line 179). I even removed that whole part 177-229, but that had no effect at all. That's the toolbox part, if I look at the contence. How is that possible? Rein