Hi everyone! I'm currently looking for a PhD and 'randomly' contacting research groups rather than hoping for an already existing project. Some researchers mention themselves that it's ok to contact them when interested, but I'm not sure about the level of formality that is needed to do that. Would they make a call just based on a motivational letter and enough info to show that my academic background is sufficient, or are recommendation letters already needed at this stage?

I haven't done this before as my PhD was at the same uni as my undergrad. But I would think that a few lines would be enough - about yourself (eg where you did your undergrad or masters and what the research topic was) and how you are interested in the work their group does - and that you would like to do a PhD there. They can then ask for more information such as CV if they are interested. This is just what I would do - I don't think there is a set etiquette. I'd be keen to hear how you get along.