hi milc, 
if you use OPENGL you can size your sketch with your screen dimensions, quit the java gray frame and location the sketch in the coordinates that you want. 
example with OPENGL: 
Quote:import processing.opengl.*;
void setup() {
  background(0);
  size(1024, 768,OPENGL);
  frame.setLocation(100,100); 
  //frame.setLocation(1280,768)/ /you can put in the other screen
}
void draw() {
  stroke(random(255));
  strokeWeight(15);
  float posy = random(height);
  line(0, posy, width,posy);
}
public void init() {
  setBackground(Color.black); 
  frame.removeNotify();
  frame.setUndecorated(true);
  frame.addNotify();
  super.init(); 
}
 
P2D or P3D mode: 
Quote:void setup() {
  background(0);
  size(1024, 768);
}
void draw() {
    frame.setLocation(100,100); 
 //frame.setLocation(1280,768)/ /you can put in the other screen
  stroke(random(255));
  strokeWeight(15);
  float posy = random(height);
  line(0, posy, width,posy);
}
public void init() {
  setBackground(Color.black); 
  frame.removeNotify();
  frame.setUndecorated(true);
  frame.addNotify();
  super.init(); 
}
 
using screen.width, screen.height 
Quote:void setup() {
  background(0);
  size(screen.width, screen.height);
  frame.setLocation(0,0); 
}
void draw() {
  stroke(random(255));
  strokeWeight(15);
  float posy = random(height);
  line(0, posy, width,posy);
}
public void init() {
  setBackground(Color.black); 
  frame.removeNotify();
  frame.setUndecorated(true);
  frame.addNotify();
  super.init(); 
}
 
best Regards
alba