Oscillometry is a popular technique for automatic estimation of blood pressure (BP). However, most of the oscillometric algorithms rely on empirical coefficients for systolic and diastolic pressure evaluation that may differ in various patient populations, rendering the technique unreliable. A promising complementary technique for automatic estimation of BP, based on the dependence of pulse transit time (PTT) on cuff pressure (CP) (PTT-CP mapping), has been proposed in the literature. However, a theoretical grounding for this technique and a nonparametric BP estimation approach are still missing. In this paper, we propose a novel coefficient-free BP estimation method based on PTT-CP dependence. PTT is mathematically modeled as a function of arterial lumen area under the cuff. It is then analytically shown that PTT-CP mappings computed from various points on the arterial pulses can be used to directly estimate systolic, diastolic, and mean arterial pressure without empirical coefficients. Analytical results are cross-validated with a pilot investigation on ten healthy subjects where 150 simultaneous electrocardiogram and oscillometric BP recordings are analyzed. The results are encouraging whereby the mean absolute errors of the proposed method in estimating systolic and diastolic pressures are 5.31 and 4.51 mmHg, respectively, relative to the Food and Drug Administration approved Omron monitor. Our work thus shows promise toward providing robust and objective BP estimation in a variety of patients and monitoring situations.