Are Convolutional Neural Networks a one model, multiple output layers.?
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.