Some applications use the mouse wheel for that behavior.
Adobe Acrobat Reader comes to mind.  When you press the
mouse wheel the cursor is changed to indicate a multi-
directional pan control that pans at a rate that increases
with the distance the mouse moves away from the original
drag point.  It's not self-centering.  The scrollbar knobs
still indicate the position within the document.

No prob.

The how and why are fairly easy once you start thinking in the Java
way (or OO way).
Think of JScrollPane as just a container for 2 scrollbars and a view.
How does it know where to put things? Simple, the ScrollPaneLayout
object
tells it.

Every panel/pane type object uses a Layout object to place things.
Some are easily hijacked (like JScrollPane) some are harder (JTable
seems to be near impossible).

In the example I used earlier I just shuffled stuff around and resized
them
every time the JScrollPane wanted an update.

See
http://en.wikipedia.org/wiki/Model-view-controller

The model can be thought of as the actual data interface (JTextArea).
The view can be thought of as the thing that controls what you see
(ScrollPaneLayout).
The controller can be thought of as the thing that handles events
(JScrollPane).

Of course the boundaries are rather fuzzy.

If you zoom in on the scroll bars then what does what is a bit
different.
Model: BoundedRangeModel (which is inside JScrollBar)
View: JScrollBar (I'm guessing via BoxLayout. Docs don't say)
Controller: JScrollBar

You should be careful with your choice of words.
People used look and "feel to mean" a wide variety of concepts.
In the Java world look and feel just means graphical look (see PLAF).

I prefer to break the GUI into three parts.
Look -
        the graphical side (does a button have the 3d look or flat?
        Is there a drop shadow? Does a button have rounded edges or
hard corners.
        Is this a red or gray or blue button.  Does it have hash
marks?

Behavior (what non-programmers usually mean by feel) -
        How does scroll bar act?
        User interaction with widgets.

Layout -
        Where stuff is placed on the screen, the size of that stuff.

Naturally there is some overlap.
And this is really just meant as an aside.
A FYI, so to speak. Take with liberal amounts of salt.

To put this in the same context as my reply above...

Look is controlled by the UIManager object and ScrollBarUI,
ScrollPaneUI, TextUI (all behind the scenes).
Behavior is controlled by the JScrollPane, JScrollBars and whatever
the JViewport is.
Layout is controlled by ScrollPaneLayout.

Well below is a basic template for DoubleScollPane.
The inner scrollbars are the standard ones.  The outer ones will be
the wacky Picassa ones.
At the moment they just sit there and don't do a damn thing.

I'm still not 100% sure of how this Picassa scroll bars will behave so
its
difficult to say on how to implement them.

You'll probablity have to make a PicassaScrollBar object that extends
ScrollBar.

Override several of the methods (maximum, minimum, BlockIncrement,
UnitIncrement, value, IsAdjusting, VisibleAmount)
and fittle with BoundedRangeModel.

Make DoubleScrollPane an AdjustmentListener for the two
PicassaScrollBars.
And adjust the view port in either the pane itself or the layout.
To be honest, I'm not sure which is the more proper.  I can see it for
either one but
I'm really not sure.  I'd guess the pane.

Here's my guess of the Picassa model:

MIN*-----A------B------C-----*MAX

When the knob is at B it has a scroll speed of 0
When the knob is at A it has a scroll speed of -x
When the knob is at C it has a scroll speed of x

So you'll have to figure out how to compute the speed based on the
position (fittle with BoundedRangeModel)

Heres the DoubleScrollPane template (its much cleaner than my original
example):

import java.awt.*;
import java.awt.event.*;
import javax.swing.*;

class DoubleScrollPaneLayout extends ScrollPaneLayout
{
    protected JScrollBar m_pHSB2;
    protected JScrollBar m_pVSB2;

    DoubleScrollPaneLayout(JScrollBar pHSB2, JScrollBar pVSB2)
    {
        super();

        m_pHSB2 = pHSB2;
        m_pVSB2 = pVSB2;
    }

    public void layoutContainer(Container parent)
    {
        super.layoutContainer(parent);

        Rectangle hRec = hsb.getBounds();
        Rectangle vRec = vsb.getBounds();
        Dimension size = viewport.getExtentSize();

        // make viewport size a bit smaller
        size.width -= vRec.width;
        size.height -= hRec.height;
        viewport.setExtentSize(size);

        // scoot VSB1 over to the left
        vsb.setLocation(vRec.x - vRec.width, vRec.y);

        // scoot HSB1 up
        hsb.setLocation(hRec.x, hRec.y - hRec.height);

        // adjust size to make the corner
        hRec.width -= vRec.width;
        vRec.height -= hRec.height;
        hsb.setSize(hRec.width, hRec.height);
        vsb.setSize(vRec.width, vRec.height);

        // set our second set of scroll bars to be
        // the same size as its partner
        m_pHSB2.setSize(hRec.width, hRec.height);
        m_pVSB2.setSize(vRec.width, vRec.height);

        // set the location of our second set of scroll bars
        m_pHSB2.setLocation(hRec.x, hRec.y);
        m_pVSB2.setLocation(vRec.x, vRec.y);
    }
}

// 2 horiz. bars and 2 vert. bars.
class DoubleScrollPane extends JScrollPane
{
    protected JScrollBar m_pHSB2;
    protected JScrollBar m_pVSB2;

    DoubleScrollPane(Component pView)
    {
        super(pView);

   
setVerticalScrollBarPolicy(ScrollPaneConstants.VERTICAL_SCROLLBAR_ALWAYS);
   
setHorizontalScrollBarPolicy(ScrollPaneConstants.HORIZONTAL_SCROLLBAR_ALWAYS);

        m_pHSB2 = new JScrollBar(JScrollBar.HORIZONTAL);
        m_pVSB2 = new JScrollBar(JScrollBar.VERTICAL);

        m_pHSB2.setVisible(true);
        m_pVSB2.setVisible(true);

        add(m_pHSB2);
        add(m_pVSB2);

        setLayout(new DoubleScrollPaneLayout(m_pHSB2, m_pVSB2));
    }
}

public class GUI extends JFrame
{
    // GUI objects
    JTextArea        m_pText;
    DoubleScrollPane    m_pScrollPane;

    public GUI()
    {
        super("Test GUI");

        m_pText = new JTextArea("This is a test.");
        m_pText.setFont(new Font(Font.MONOSPACED, Font.PLAIN, 12));

        m_pScrollPane = new DoubleScrollPane(m_pText);

        add(m_pScrollPane);
        pack();
    }

    public static void main(String[] args)
    {
        GUI pApp = new GUI();

        try
        {
   
UIManager.setLookAndFeel(UIManager.getSystemLookAndFeelClassName());
            SwingUtilities.updateComponentTreeUI(pApp);
        }
        catch(Exception ex)
        {
            System.out.println("Java's PLAF is fubar");
        }

        pApp.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        pApp.setVisible(true);
    }
}