I have decided to split my project into two boards: one board is circular and holds the LEDs; the electronics will be on a rectangular board in the base of the project, with four wires (+V, R, G, B for common anode RGB) going from the electronics board (Nano, 3 MOSFETs, 6 resistors) to the display board (24 RGB LEDs). So I have to split the schematic. No big problem there. But I went looking for an offboard connector pad (wires will be soldered, not plugged in) and could not find a simple pad with a hole in the middle that I could run a wire to. What does Fritzing call this? I tried “connector”, “offboard connector”, “pad”, and nothing useful showed up. Also, it keeps insisting on wanting the three potentiometers on the board, and I want to just run five wires to the pots (+V, GND, R, G, B), and there does not seem to be a way of accommodating offboard components while having them in the schematic.
The easiest is probably the “Hole” part. Look at the “CORE” bin. Second group from the bottom is “PCB View” which contains several parts that can be used for this. The Hole part allows setting the size of the hole, and the thickness (width) of the copper ring around it. A via could also work. I have never tried those with a single sided board, so verify.
Fritzing does not “insist” that a part is placed anywhere specific. When a part is added in one view (schematic in your description), that part is also shown on the other views, but the “initial” position is somewhat random. Drag it to where you want, including to a second board, or off of the boards completely. If a part is totally “off board” for PCB view, drag it away from the board, and manually add a connectors (or Hole parts) to run wires too. Even if being soldered directly, without a header, the “Connection” part (from CORE bin) is handy. It allows one or several connections to be placed with specified spacing. Wires can be directly soldered to those, instead of soldering a header to connect to. Fritzing does not know or care what (if anything) is later soldered to the pads that have been defined.
When working with more than one board in a project, some operations require one of the boards to be selected, and the operation applies only to that board. Design Rules Check for example.