There is no official answer in the manga, but I can speculate that they pulled a Riener and simply bit the nape of the Titan and talking there powers (and life) and might have waited 13 years or would have just killed them outright to separate the powers, there could have been constant attacks and threats to the titan shifters so, this also might explain the reason the Ackerman family came to be. We know one thing though, King Riess said he was horrified at the atrocities of his ancestors or something along those lines. There was probably a ton of backstabbing, and so, over time that enabled Marley to eventually acquire 7 out of the nine titans.
Hope this helped, sorry it took so long for an answer to your question. I'm new.