THAT'S what I really wanna know! What effect does it have on the children? And what rights does a Sperm Donor have to his children? I sure wouldn't mind meeting my kiddies someday!
First off, you are going about this all wrong. You need to ask an actual authority on the subject firsthand and get a rundown on all of the correct information. Go into a clinic and ask to see the paperwork that you have to fill out. And ask if you can view the documents that the mother has to fill out in order to get the donated sperm.

As far as I know, you have no obligations towards the child. I am sure there are waivers signed to prevent the mother from getting child support from the sperm donated, but that is just an assumption based on logic.

As far as the psychological effect that the information would bring onto a child, that is entirely unknown to anyone. People react to information in incredibly different ways based on a variety of different factors. Least of which are how their parents react to situations. The enviroment in which the child grows up in and the ways they are raised, influences in a persons life, those are the sorts of things that influence a reaction such as the one you are asking about.

Also take note that just because you are a supposedly beautiful and intelligent human being, that does not mean the child will be. You must take into account that the mother is going to provide half of the genes that the child will get, and perhaps the number will be higher depending on certain circumstances. Some people look more like one parent, or take more after one parent, than other children do.

Also, having contact with the child would probably be entirely up to the mother until the child has reached the age of adulthood. Then, and only if the child found out through whatever means, would they be able to decide whether or not they want to meet you. I do not think you are privy to any information on the mother, child, or condition of your sperm.

Oh, and even if this limit of 10 does exist, there are always the chance of multiple babies being born. Twins, triplets, quadruplets! Woohoo.