At Dartmouth College, computer science started as a branch of the Mathematics Dept. It was eventually made it's own department (located in a former clinic for the mentally ill, Sudikoff Laboratory which some see as ironic). Now Dartmouth is building a new addition to the engineering building (Thayer School of Engineering) and the Math and Computer Science Dept's will move there. I believe the thinking is that those dept's collaborate so much that having them located in the same complex will be helpful. Much of computer science research is more about applications of computers rather than research into computing itself, though some pure computing theory is still being worked on, and everything is becoming cross disciplinary across many fields. One CS project I worked on was designing a smartwatch for health apps. It involved electronics engineering, operating system development, health applications development, sensor data processing, medical research on senior frailty, gesture UI design, UI usability research, secure wireless data transport and collection and more. It was run by a CS prof though. If you go into CS you can end up working on anything and everything. Another CS robotics project involved electronically herding cattle. Where do cattle fit into CS theory? As end users of computers? :-)
At Harvey Mudd College, when I was there in the 80s, the Computer Science department was part of the Biology department: They had one prof who did CS exclusively, one who did Biology exclusively, and one who did both. The “real” departments, Mathematics, Physics, Chemistry and Engineering all offered the option to do a CS option within them, but one of the cool things about Mudd of that era (I’m not sure how much of this has survived since then), was that you didn’t really do a specialized degree in Math, Physics, etc. but got a good broad education across the discipline.