Unconstrained handwritten text recognition remains an important challenge for deep neural networks. These last years, recurrent networks and more specifically Long Short-Term Memory networks have achieved state-of-the-art performance in this field. Nevertheless, they are made of a large number of trainable parameters and training recurrent neural networks does not support parallelism. This has a direct influence on the training time of such architectures, with also a direct consequence on the time required to explore various architectures. Recently, recurrence-free architectures such as Fully Convolutional Networks with gated mechanisms have been proposed as one possible alternative achieving competitive results. In this paper, we explore convolutional architectures and compare them to a CNN+BLSTM baseline. We propose an experimental study regarding different architectures on an offline handwriting recognition task using the RIMES dataset, and a modified version of it that consists of augmenting the images with notebook backgrounds that are printed grids.