If you're prior-enlisted infantry, is it almost always certain you will branch infantry at OCS?

Short answer: No.

The biggest impact to what you can branch is determined by "the needs of the Army" at the time the branch selection is determined. Since you have absolutely no control over that, you already keyed in on what gives you the best shot at branch selection that you can control - your OML.

What goes into the OML at OCS? Pretty much everything that has a grade/score attached to it as well as subjective evaluations (positive and negative) that the commander has reviewed and approved.

Brach selection is done by the Accessions Branch at HRC, not at the OCS course you attend. The OCS course leadership sends your packet up to HRC where a selection board will review your packet, your OML and make a decision based on the following:
● "Needs of the Army" (Branch quotas)
● Personal preferences of the candidate
● Educational background
● Prior military training and experience
● Physical qualifications

So, will being prior Infantry as enlisted edge you towards being branched as an Infantry officer? Yes, but it's only one of many factors.

Combat Arms will usually have the largest Branch quotas for the selection board, so proportionally the majority of the candidates will be branched into Combat Arms.
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* https://www.hrc.army.mil/Officer/Officer%20Candidate%20School
* https://armypubs.army.mil/epubs/DR_pubs/DR_a/pdf/web/r350_51.pdf

I am told that today that Infantry is one of the competitive branches and you would need to be at the top or close on the OML to get it. Not the case in my day. I volunteered for it, I was already a grunt. However, a lot of the people that went through Infantry Officers Basic Course with me did not have Infantry as their first choice, or top three

Not really. Ultimately it is the needs of the Military and more specifically the needs of the branch of Military.

There are fewer officer billets per respective MOS than enlisted. Combine that with Infantry generally being a big draw it's way more competitive. MOS selection for Officer's overall is pretty competitive with certain jobs being a bigger draw than others. The only thing that cuts the line are jobs with specific eligibility criteria and a separate pipeline such as aviation/medical field/Chalain.

I would think that you would apply to the OCS for the branch you want, for example, Signal is at Fort Gordon, FA at Fort Sill, etc. If you do not want Infantry, do not go to the Benning School for Boys. They are so far behind that last I heard they still had Follow Me for a slogan. Rest of the Army is After You so that leaders can look over what happening in front of them and not have to turn around and look behind them. LOL

Very few in OCS get what they want for branch