On desktop based browser application there are elements which allow us to do a multi selection, like below:
Is there support for this on touch-based phones? How do these kind of devices simulate the CTRL keypress?
On the major three mobile platforms' default browsers, it appears as though multiple select listboxes are supported just fine. They each implement the functionality similarly. What actually happens is you click the form element and a modal dialog is presented with a scrollable list of your options and a way to select them.
I would say all of which are actually a great improvement over the desktop interaction pattern of using ctrl-click.
I could only find a screenshot of Android's implementation (here), but I have a Windows Phone and iPad which I used to confirm the functionality on those platforms.