Will choosing a specific department or major improve your chances?

For admissions at PENN, would you stand out slightly applying for a unique major? Would specific departments be more interested in getting students? Say, even if you are interested in law/prelaw, and have a range of majors to choose from that you are genuinely interested in…what departments give you a more unique profile/higher chance?

No. Penn admits by school - College, Wharton, SEAS, Nursing. Other than that, your choice of prospective major is not what will get you admitted. Half of all admitted students change their mind before settling on their major, so Penn is not using the application for planning and budgeting purposes.
https://www.college.upenn.edu/prospective-faq

Also, (generally, not limited to Penn) if choice of major or division matters for frosh admission, the more selective major or division will have a secondary admission process to change into it later after enrolling, because it is at or near capacity and can take in few or no additional students.

Admissions officers are well aware of the fact that you can apply for one major and change to any other major that is within the college you have been admitted to once you start. I’ve heard a number of college admission officers (including some from Ivy and equivalent schools) say that they don’t pay much attention to intended major in the admission process since about half of the applicants apply undecided and about 50% of those coming in with a designated major end up switching it while they are at college.

There could be an exception if a student has a long standing and very strong demonstrated history of interest/aptitude (perhaps through ECs, research, classes etc.) in some obscure major.

Keep in mind that any ploy you come up with to try to get an edge in admissions, college adcoms have seen thousands of times over. IMO your time would be better spent searching out a group of reach, match, and safety schools based on your academic stats that appear affordable and that you would be happy to attend.

Well, here’s the contrary comment. Yes, it can help to want an under-enrolled major. No, it won’t help one whit if your record doesn’t show both thorough prep and grand engagement outside class for the major(s) you state. Not at a tippy top.

To change majors at College X, first you need to be admitted. Your app needs to make sense. This isn’t just saying you want some major that needs students. You need to show you are ready to hit the ground running. I don’t think 50% of applicants are saying undecided (and what proportion of those get admitted.)

A lot of getting into a tippy top is the quality of your thinking, how that drives you/has been driving you. No easy shortcuts. It takes a boatload of savvy to game.

Ime, even kids who do say undecided are vetted for where their strengths (and implied interests) lie. You make choices in hs. This is, “Show, not just tell” and your record shows the stuff or not.

They can pay a lot of attention to stated major interests. It forms a context for assessing.