So this is a serious question/request. I fear I may be very distantly related to one of the "royal" families of old. It kinda makes me sick to be honest. It would probably cause me emotional harm if I am indeed distantly related to the illuminati. I don't want evil blood.
If it matters, it's one of the Italian Houses. There's a few popes and cardinals with the maiden name in my family. I haven't bothered searching yet but I already feel down about it.
Any search you do using the internet is trackable. If you want to do family searches that are not, you must do it the old fashioned way - travel and search the libraries. My cousin did it for years and amassed a mountain of documentation. All done without the internet. There is no way to conduct an ancestry search from the comfort of your home without using internet resources. So, I hope that answers your question.
Just one word of caution about using things like ancestry.com. Many of the family trees established by others are not necessarily accurate. People are lazy when it comes to research and just assume that others have done the work that they then piggyback on. They will then take that information and continue the dissemination of family trees that may be flawed or completely in error. Do not make that mistake. Unless there is a paper trail so to speak to verify information from multiple sources if possible, never use the information found in other family trees as a sole source of verification. Their information can be used as a springboard to your own digging, but it should never rest solely there.
Researching family ancestry is a time consuming endeavor and not a mere curiosity. So, if you are not willing to put the time in to know, then I would suggest finding someone that has taken the time to do the research and see if they will share it with you. My own personal experience with ancestry researchers is that they are very greedy with the information they have. They often are not willing to give away all of the time and effort they have invested in the work that may have taken years to collect. So, don't expect too much in the way of detailed information. But, if all you have is a general curiosity, that may suffice for you.
Also, any American that has a family history of length from the times of colonization and prerevolution, will have links to royal houses in Europe. I have several. It only stands to reason that in the beginning, people with resources were the main European transplants - that means that their money is what financed the trips. Poor immigrants came as either slaves or indentured servants. The huddled masses of immigrants from very modest means came later in our history. The founders were generally families of substance from either wealth or merchant class that established a colonial beachhead in the new world. Their children and grandchildren were the ones that broke ranks from the old world - something their ancestors would never have thought to even contemplate despite differences in opinions.