Plasmas with zero or near-zero current density in a wide region of the core have been produced in DIII-D discharges. The discharges were obtained with early neutral beam and electron cyclotron heating (ECH) during the plasma current ramp. Wide current holes (CHs) with a near-zero field over about 23% of the plasma width and narrow CHs with a duration of up to 1.1 s (comparable to the current relaxation time) have been obtained. Equilibria and pressure profiles were obtained by including kinetic and motional Stark effect (MSE) data using the code TRANSP. Agreement between calculated and measured neutron fluxes is obtained only when the fast-ion diffusion coefficient is set to very high values which results in considerable fast-ion redistribution and a broadened pressure profile. The MSE-only equilibrium fits are in good agreement with such kinetic fits. While CHs collapse due to tearing modes, bursty MHD activity coherent with electron temperature relaxation events is observed when the CHs are sustained. Some collapse events also appear to be coincident with edge localized modes. The CH phase seems to have been limited by the no-wall beta limit. In the present set of discharges, wider CHs (steeper temperature gradients) appear to collapse at somewhat lower β. Tearing modes are seen to cause shrinking of the CH. While early electron heating is strongly dependent on the timing and power of the neutral beam and by the ECH power, it is seen that larger neutral beam powers are correlated with wider CHs which do not decay significantly. An extensive and perhaps difficult analysis of current transport is required to check whether a neoclassical poloidal flux evolution (diffusive EMF) is either consistent with a stationary current profile or that an additional or anomalous EMF is present.