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In this paper, we consider partitioned edge learning (PARTEL), which implements parameter-server training, a well known distributed learning method, in a wireless network. Thereby, PARTEL leverages distributed computation resources at edge devices to train a large-scale artificial intelligence (AI) model by dynamically partitioning the model into parametric blocks for separated updating at devices. Targeting broadband channels, we consider the joint control of parameter allocation, sub-channel allocation, and transmission power to improve the performance of PARTEL. Specifically, the policies for joint SUbcarrier, Parameter, and POweR allocaTion (SUPPORT) are optimized under the criterion of minimum learning latency. Two cases are considered. First, for the case of decomposable models (e.g., logistic regression), the latency-minimization problem is a mixed-integer program and non-convex. Due to its intractability, we develop a practical solution by integer relaxation and transforming it into an equivalent convex problem of model size maximization under a latency constraint. Thereby, a low-complexity algorithm is designed to compute the SUPPORT policy. Second, consider the case of deep neural network (DNN) models which can be trained using PARTEL by introducing some auxiliary variables. This, however, introduces constraints on model partitioning reducing the granularity of parameter allocation. The preceding policy is extended to DNN models by applying the proposed techniques of load rounding and proportional adjustment to rein in latency expansion caused by the load granularity constraints.