kNN - what happens if more than K observation have the same distance to the centroid of the cluster EDIT It was pointed out in the Answers-section that I am confusing k-means and kNN. Indeed I was thinking about kNN but wrote k-means since I'm still new to this topic and confuse the terms quite often. So here is the changed question.

I was looking at kNN today and something struck me as odd or - to be more precise - something that I was unable to find information about namely the following situation.

Imagine that we pick kNN for some dataset. I want to remain as general as possible, thus $k$ will not be specified here. Further we select, at some point, an observation where the number of neighbors that fulfill the requirement to be in the neighbourhood are actually more than the specified $k$.

What criterion/criteria should be applied here if we are restricted to use the specific K and thus cannot alter the structure of the neighborhood (number of neighbors). Which observations will be left out and why? Also is this a problem that occurs often, or is it something of an anomaly?
K-means does not make an assumption regarding how many observations should be assigned to each cluster. K is simply the number of clusters one chooses to generate. During each iteration, each observation is assigned to the cluster having the nearest mean. There is no assumption that all clusters should have a comparable number of observations assigned (i.e., for N observations, there is no expectation that each cluster should have ~ N/K observations assigned).

It is quite possible that the numbers of observations in the various clusters are highly imbalanced. This can be due to the distribution of the data, the number of clusters chosen (K), or even how the cluster means are initialized.