The parameter adaptive control problem of linear stochastic distributed-parameter systems is considered and treated by invoking the partitioning/non-linear separation approach. Both continuous-time and discrete-time systems are studied, with volume and/or boundary control and disturbance inputs. The following cases are considered: spatially-continuous and point-wise measurements/control actions, continuous and quantized parameter space, non-gaussian initial state, uncertainty in continuous and point-wise measurements, cost-function with spatial-derivative penalties, systems with pure time delays, composite distributed- and lumped-parameter systems, scanning-type control, and simultaneous adaptive system and measurement control. The uncertain parameters are assumed to be time-and-space independent, but the spatial independence can be alleviated as will be shown elsewhere.