TouchNow streams your Mac's screen to an iPhone or iPad and lets you control it by touch — or play Mac games on it with an on-screen controller.
Three modes: trackpad (like a MacBook's), direct touch (tap the screen and it clicks that spot on your Mac), and game controller. The on-screen controller maps to keyboard input, so Mac games that only expect WASD work without any changes. Layouts are fully customisable, and there's an optional retro handheld shell (four shapes, ten colours, two with twin analog sticks). Plug in a real controller and it takes over automatically.
Free forever on your own Wi-Fi: devices find each other automatically, with no account and no router setup. Remote access over the internet is a subscription (US$2.99/month).
Unlike Apple's Sidecar, it works with iPhone (not just iPad), works across networks, and can turn your iPhone into a real second desktop rather than a mirror. It can also wake a sleeping Mac remotely and keep streaming while the Mac is locked.
The Mac side is a free download from touchmac.app (Developer ID signed, not on the Mac App Store). The iOS app is on the App Store.