Neurons execute diverse computations that are constrained by the branching of their dendrites and the synapses they form with other neurons. During brain development, many dendrites grow simultaneously and become integrated into multiple networks. Extensive experimental data has demonstrated the role of synapse formation and neural activity on dendrite growth. Yet, computational models of dendrite growth mostly assume random branching, implement activity-independent growth cones or generate dendrite morphologies based on abstract mathematical constraints. While these approaches achieve highly accurate dendritic morphologies and capture the dendrite's developmental stages, they lack mechanistic insight into how changes in morphology influence and constrain the emergence of function and vice versa. Consequently, they fail to elucidate the link between morphological variability and electrophysiological or functional properties. Here, we propose a model in which dendrite growth and retraction stem from combining activity-dependent and -independent cues from potential synaptic partners. A newly formed synaptic contact is either stabilized or removed according to a local plasticity rule for synaptic organization. Consistent with experiments, three sequential phases (overshoot, pruning, and stabilization) emerge naturally in this model. Furthermore, growth is perturbed in a biologically-plausible fashion when the local plasticity is perturbed. Since input correlations determine synaptic stability, dendrites achieve selectivity to correlated inputs by pruning uncorrelated inputs. In our model, this selectivity of individual dendrites leads to competition for appropriate synaptic input between nearby dendrites and affects dendrite morphology in an experimentally-testable way. Furthermore, dendrites acquire diverse morphologies despite nearly identical initial conditions, highlighting how early developmental variability affects mature morphology. Since proximity to potential synaptic partners controls dendritic outgrowth in the model, dendrites approximate optimal wiring length but overshoot it slightly. In summary, our mechanistic model captures diverse phenomena related to dendrite growth and suggests specific ways in which synaptic formation and removal control both form and function.