To predict the shape of solidifying material onto a substrate is currently motivating an increasing number of studies related to additive manufacturing. Here we consider the solidification of a liquid drop on a cold substrate, below the freezing temperature, under continuous feeding at a constant flow-rate through a thin needle placed above. We compare experimental shapes to those predicted by a theoretical model where heat transfer is mainly due to conduction within the solid and when the inner flow is neglected. Hence, this is an analogous of Stefan problem for a sessile drop, with additional feeding of liquid. We show that, depending on the control parameters, namely the initial angle, substrate temperature and flow-rate, different shapes are observed, in particular original overhanging ones. We provide a simple model, which is in very good agreement with experiments. We then discuss on the limitations of the model.