The signal and noise in lateral T-shaped spin-valve structures is investigated from a theoretical point of view in the diffusive regime. Due to the T shape of the investigated device it is found that the nonlocal signal is strongly influenced by the width D of the spin-conducting channel, varying substantially on a lateral length scale of the order of the spin-diffusion length ℓsf. This effect demonstrates the influence of two-dimensional dimensionality on spin transport in the spin channel and, in particular, the strong impact of not only the device size but also of the device shape on the nonlocal signal. The nonlocal signals in the longitudinal and transversal directions of the spin channel are calculated as a function of the angle between the magnetization of the various injecting and collecting magnetic electrodes. In addition, the various sources of noise induced in the lateral spin valve are discussed with a particular attention on the noise due to the thermally induced fluctuations of the spin-accumulation vector in the paramagnetic spin-conducting channel. An explicit expression of the dependence of the signal-to-noise ratio on ℓsf in the paramagnetic spacer and on its dimension is obtained. Implications for the use of such lateral spin valves as sensors in read heads for hard-disk drives are discussed.