How can I slideDown with #states? I have a form using "#states" (in the Relation module), and it works, but it kind of jumps around. A nice slideDown would be so much better. 

How can I do that instead of just making it visible?
I assume you're using the visible state?

The code that is responsible for doing this is in states.js:

$(document).bind('state:visible', function(e) {
    if (e.trigger) {
      $(e.target).closest('.form-item, .form-submit, .form-wrapper')[e.value ? 'show' : 'hide']();
    }
  });


As you can see, it calls show/hide without any configurable parameters, which means that it can't be easily changed.

However, the comment above that block is interesting:

/**
 * Global state change handlers. These are bound to "document" to cover all
 * elements whose state changes. Events sent to elements within the page
 * bubble up to these handlers. We use this system so that themes and modules
 * can override these state change handlers for particular parts of a page.
 */


If I understand this correctly, you can override the event handler for your specific page element, e.g. the form or even single form elements, by adding something like this:

$('form.your-form-class').bind('state:visible', function(e) {
  if (e.trigger) {
    $(e.target).closest('.form-item, .form-submit, .form-wrapper')[e.value ? 'slideDown' : 'slideUp']();
  }
});


I guess you will need to return FALSE to prevent that the event bubbles up further in the DOM tree.