I'm not sure if there's a direct way to limit the capacity of a JTextArea.
I'd be a little surprised if there was and don't see anything like that in
the API. But maybe I just didn't look carefully enough.

However, a less direct approach seems very possible. One of the methods that
JTextArea inherits from JTextComponent is getText(); it returns a String
that has the contents of the JTextArea. Therefore, if your JTextArea is
called myTextArea, myTextArea.getText().length() will tell you how many
characters you have in your JTextArea.

You could use a Caret Listener to detect when the caret (cursor) for the
JTextArea indicates that the JTextArea is over a certain size; if that
happens, you can use the select() method of JTextComponent to find a desired
part of the JTextArea - the first 100 characters, for example - and then
remove those characters, presumably after writing them to somewhere
permanent if you still want the information in them. The easiest way to
remove them from the JTextArea would appear to be the cut() method of
JTextComponent.

You should be able to find all of the necessary techniques in the Java
Tutorial in the section about text areas or the section on caret listeners.

--
Rhino

Some of the JTextArea constructors take a Document argument.  Use the
Document class below to set the size limit on your JTextArea.

//
//
//  LengthLimitedDocument
//
//

import javax.swing.text.*;

public class LengthLimitedDocument extends PlainDocument {
    protected int limit;

    public LengthLimitedDocument(int limit) {
        this.limit = limit;
    }

    public void insertString(int offs, String str, AttributeSet a)
     throws BadLocationException {
        super.insertString(offs, str, a);
        int length = getLength();
        if (length > limit)
            remove(0,limit/20);  // remove 5% of document if over limit
    }
}