Are Convolutional Neural Networks a one model, multiple output layers.? I'm writing a university report on for the Toxici comment classification Kaggle competition, comparing different attempt made with different models and I want to know if Convolutional Neural Networks are One model, multiple output layers model.

ONMO are also known as multi-task learning, this approach would have one input layer, one set of hidden layers, and one output layer for each label.

On the other hand, CNN are several layers of convolutions with nonlinear activation functions like ReLU or tanh applied to the results. It uses convolutions over the input layer to compute the output rather than a fully connected layer, or affine layer.
Convolutional neural networks implement the convolutional filter technique. This is more or less a sliding window, usually (but not limited to) convolving across the width, heights and depths of images. 

If you have a single task or multi learning learning task depends on what you want this network to output. Convolution rather describes the behavior of a single layer processing some inputs into some intermediate outputs. The characteristics of your last layer determine if it is used for single or multi tasks. To my understanding this is rather independent of the convolution.