How to make Application’s windows always display in the same Monitor when having multiple displays

There are endless ways to do this, so here are a few:

• Before you unplug the external monitor open up the Displays Preference Pane in System Preferences and click on the "Gather Windows" button.

  [or if you already unplugged]

• Hold the Option key down and choose "Arrange in Front" from the Window menu.

  [or]

• Use the Option key and click the (+) at the top of any Finder window and it will resize them all automatically.

This Applescript script might also work:

tell application "Finder"
-- get desktop dimensions (dw = desktop width; dh = desktop height)
set db to bounds of window of desktop
set {dw, dh} to {item 3 of db, item 4 of db}
end tell

tell application "System Events"
repeat with proc in application processes
tell proc
repeat with win in windows
-- get window dimensions (w = width; h = height)
set {w, h} to size of win

-- get window postion (l = left of window; t = top of window)
set {l, t} to position of win

-- nh = new window height; nw = new window width
set {nh, nw} to {h, w}

-- window width is bigger than desktop size,
-- so set new window width to match the desktop
if (w > dw) then ¬
set nw to dw

-- window height is bigger than the desktop size (minus menu bar),
-- so set new window height to be desktop height - 22 pixels
if (h > dh - 22) then ¬
set nh to dh - 22

-- r = right coordinate of window; b = bottom coordinate of window
set {r, b} to {l + nw, t + nh}

-- nl = new left coordinate; nt = new top coordinate
set {nl, nt} to {l, t}

-- left coordinate is off screen, so set new left coordinate
-- to be 0 (at the left edge of the desktop)
if (l < 0) then ¬
set nl to 0

-- top coordinate is above bottom of menu bar (22 pixels tall),
-- so set new top coordinate to be 22
if (t < 22) then ¬
set nt to 22

-- right coordinate extends beyond desktop width,
-- so set new left coordinate to be desktop width - window width
if (r > dw) then ¬
set nl to dw - nw

-- bottom coordinate extends beyond desktop height,
-- so set new top coordinate to be desktop height - window height
if (b > dh) then ¬
set nt to dh - nh

-- if we have calculated a new top or left coordinate, reposition window
if (l ≠ nl or t ≠ nt) then ¬
set position of win to {nl, nt}

-- if we have calculated a new height or width, resize window
if (h ≠ nh or w ≠ nw) then ¬
set size of win to {nw, nh}
end repeat
end tell
end repeat
end tell

Of course there's also the paid alternative, which might include Stay, Divy, Arrange, etc.

Update: There are now several competitors, such as Luna Display, as well as native support in iPadOS 13 + macOS Catalina, called Sidecar.

The app Duet Display lets iOS devices connect to a Mac that is running at least OS 10.9. The Mac needs duet software which is a free download and connects via Lightning port to the Mac in question to send the video.

The Mac app is a free download and the iOS app is available for purchase on the iOS App Store.